Ahh, what a question.
Most anime that I like would have its reality checks bounce. If I want reality, well, I live in it. The short version of an all-inclusive reality check would be that giant mecha are stupid (any technology that allowed them would be even more effective used in other more conventional weaponry), magic and ki and psi don't exist, human beings CAN'T take that kind of beating and keep going, let alone fully recover, no, it's not possible to be that accurate with a sword or other hand weapon, and Law of Action and Reaction, Baby!
To choose a specific subgenre is hard. There's so many. But I'll choose one and just note that my comments here really could apply to many others, with minor modifications.
And I choose the ki warrior subgenre, which includes DB/DBZ, Naruto, Street Fighter, and in a more general sense most of the superpowered five-team shows like Saint Seiya, YST, Shurato, etc.
Now, this genre can't EXIST without ignoring a lot of reality, so my "reality check" will here be more an "internal logic awareness" check, because THAT'S the part that annoys the hell out of me in this or other genres: saying Stuff That Makes No Sense Even In Your Weird Universe.
The most common of these things is No Sense of Scale; a character (who should be in a position to know) will make a numeric or at least quantitative statement about some aspect of their abilities, and even a cursory examination of the way things then play out show that he was completely full of S**T, or that he was leaving out huge swaths of information which would have made that statement probably a lot less impressive. For instance, in Saint Seiya, Gold Saints are stated to move "At the Speed of Light". Other Saints, even Silvers, are described more as moving at Mach numbers, and not very high ones (maybe in the low 10s).
Lightspeed is about Mach 880,000. We already know what the effects of things moving at vastly lower speeds -- like meteors, going at what might be Mach 50-60 -- are like. So Mr. Lightspeed should DEVASTATE THE CONTINENT just by BLOCKING. Or hell, just by moving at Gold speed.
More, the difference in power and speed between the Golds and the Silvers makes the differences between Silvers and Bronzes, or even Silvers and ordinary overweight geeky human beings like me, look like NOTHING. If a Silver Saint is going at Mach 20, he's 44,000 times slower than the Gold. By human comparison, this is the difference between me having an all-out sprint speed of maybe 15mph, and something that can go all-out and achieve 43 FEET in ONE DAY. A paramecium (a one-celled ciliate) can go at about 1mm/sec -- which is about 7 times faster than 43 feet per day! The fights between a Gold who actually intends to WIN and a Bronze or Silver should be over before either of the lessers even knows it.
And then there are the typical Saint bragging speeches... in which at least once a character says "My lightspeed is faster than yours!" *HEADDESK*
Dragonball Z hits other areas of this problem. They introduce a technology called a "Scouter" which produces power readings. Trying to make SENSE of these power readings will give you fits if you think about it too long.
Partly this will be due, once more, to a complete lack of scale understanding. Early on in Dragon Ball, Kame-Senin was confronted by Goku transforming into an Oozaru -- a monstrous, gargantuan monkey-like monster -- which was a werewolf-like transformation. That is, it was triggered by the full moon. Rather than kill Goku, Kame-Senin BLEW UP THE MOON.
Blew. Up. The. Moon.
Other power feats to that point had included things reaching the level of blowing away a mountain, making craters in the ground, etc. The "MAX POWER KAMEHAMEHA!" wasn't just kicking it up a notch, it was going from bland oatmeal to purified capsicaicin in one swell foop. The amount of power needed to blow up even a minor planet-sized object like the Moon (~2,000 miles across) is absolutely mindboggling. And doesn't fit at all with the power scale we see people throwing around on a daily basis.
But let's say that there's an explanation for this -- maybe non-living matter is SO much more vulnerable to ki-energy that you can destroy the moon with energies that, used against a living opponent, will just end up putting him through a few mountains.
We still end up with the problem of numbers -- because Kame-Senin gets rated so low on the totem pole that he almost doesn't matter at all, and Goku and Vegita hit between 10,000 and 20,000 by the end of their first throwdown -- while Freezer is rated at 100,000, but still seems to have to crank things up to blow up a planet, which Kame-Senin's prior achievement would indicate should be absolutely TRIVIAL by that point.
(And even within the show this is waffled over; sometimes planets seem to be easily destroyed pinatas, sometimes them being destroyed is impressive)
Scaling affects a lot of things, but in combat shows it's pretty egregious when you have someone take blows clearly capable of knocking down skyscrapers, and be only partially shaken, and then get taken down by being hit with a large rock.
The other area in such super-powered shows that can be very annoying is Never Using Your Resources. Sometimes, as in Saint Seiya, there's a mystical ritualism which constrains the characters from doing certain things (like deliberately ganging up on each opponent) but in many others that's not the case. Moreover, there are many cases in which even a minor application of thought would show you that you could get a lot more bang for your buck by using Power X and Power Y TOGETHER in a particular combination, but no one ever thinks of it. The fact that sometimes these tricks ARE thought of and used (for instance, in Naruto when the fact that Naruto can make HUNDREDS of duplicates of himself that TRANSFER memory and experience BACK to the original when killed or dismissed is used to allow him to train up, and later to scout out capabilities of opponents) just makes the other failures more obvious.
Oh, and speaking of NARUTO, here's one of the worst FAILs of all in that area: Inconsistent Worldbuilding. In some ways Naruto's world is a very interesting exercise in worldbuilding; the creator has clearly worked hard to make a set of super-martial disciplines which have both breadth and depth and mechanical functionality to them that allows him to tell stories that actually involve strategy on the part of the characters. And often he does this well. But....
... then he has a society in which there are no guns. But they have bombs. There are no factories, large cities, etc.... and Naruto comes home to switch on the lights in his home using a flat rocker-style switch that implies an immense manufacturing infrastructure. They have CD/DVD players and televisions... but they haven't got phones and long-distance radio, relying on CARRIER BIRDS to bring information from one village to another??
Making high-tech gadgets like CD players implies a *HUGE* amount about your civilization -- its level of advancement and its overall size, and the size of a MARKET necessary to support mass production of such devices. It implies all sorts of precision and control in manufacturing, in the ability to mine and refine metals and synthesize plastics from oil, etc.
But here they are, using 20th/21st century gadgets whenever it amuses them, they have black-powder bombs and explosive runes but no guns, they have power generators for lighting the city and powering all sorts of other things but nary a car nor a plane to be seen. It's INSANE! What, do they have a Summon DVD Jutsu? A Manufacture Power Generator Jutsu? Then why not a B-1 Bomber Jutsu?
Ahh, there, I've gotten all that out. Felt good.
Day 1 - Very first anime:Saint Seiya
Day 2 - Favourite TV series: : The Vision of Escaflowne
Day 3 - Your anime crush: Belldandy, from Ah! Megamisama/Ah/Oh My Goddess! and Shun from Saint Seiya
Day 4 - Favourite Film: Tonari no Totoro/ My Neighbor Totoro
Day 5 - Anime character you feel you are most like (or wish you were): Shikamaru from Naruto Shippuden
Day 6 - Most annoying anime character: Mihoshi, Tenchi Muyo!
Day 7 - Character you’d most like to slap: Sasuke, Naruto Shippuden
Day 8 - Most epic scene ever: End battle of YuuYuu Hakusho: The Poltergeist Report Movie
Day 9 - Saddest anime scene: Belldandy erasing herself from Keiichi's life in Ah! Megamisama/Ah/Oh My Goddess!
Day 10 - Favorite slice of life anime: Koko wa Greenwood
Day 11 - Favorite mech series: Giant Robo: The Day The Earth Stood Still
Day 12 - Best instalment of a franchise you don’t like: Nihao My Concubine
Day 13 - Worst instalment of a franchise you do like. Dragonball GT
Day 14 - Current (or most recent) anime wallpaper: Picture of Son Goku with Shen-Long done by my wife Kathleen
Day 15 - A reality check for a genre you like : Power-warrior anime and internal sanity/consistency!
Day 16 - An anime classic that simply doesn’t work for you.
Day 17 - Best Background Music
Day 18 - Best Five-team (?)
Day 19 - Change you’d like to make to any one anime
Day 20 - Most ambiguous anime character
Day 21 – Favourite OAV Series
Day 22 - Animation studio you'd most like to slap.
Day 23 - Anime you think had the best, or most intriguing art
Day 24 - Favorite anime hero or heroine
Day 25 - Best anime villain
Day 26 - Your favorite harem anime
Day 27 - Favorite anime opening theme song
Day 28 - Favorite anime companion/summoned creature
Day 29 - Best Anime Music Video
Day 30 - Favorite anime ending theme