The thing is, there is no surefire way to check if something is random at any individual point in time. The only data you can gather is from previous shufflings, but that data doesn't matter, because the only data that matters is the shuffle you make right now, not the one after, not the one before.
People must realize is with random, what you get is what you get. You can't force something to be more random when it is already random, such as, you don't see any clumps, so you shuffle again until you get clumps. That isn't how it works. The fact that you didn't get clumps is the fact that it is random, and because the randomness picked a order of cards that doesn't have any clumps. That's what random is.
There is no such thing as not having certain combinations because it is random. It may happen less, it doesn't mean that it does not happen that you have to reshuffle your deck because it isn't random, because the fact is that, the deck is random.
The mistake I see people make here is that they use data from other shufflings when that data does not count. You only count the shuffle you make now, and not any shuffle. The only data to make is probably if you constantly get the same order of cards, then yeah, there is a problem, but just because you don't get clumps in one shuffle out of many doesn't make the deck not shuffled randomly.
The other thing is deck makeup. If a person's deck is built in a way that by randomness, you don't get clumps, ahem, singleton decks, but who makes those anyway, then they shouldn't be labeled a cheater because they built a deck a certain way.
The thing with random is you want to lose control over where your cards end up, hence saying, when you shuffle, don't think. By trying to make the deck more random, you are inadvertently controlling where the cards to go through your preconception of "random", and therefore, you aren't make your deck random. By doing that, you are thinking. Don't think. Just shuffle, and if you don't think, and don't look at your cards, even if the deck wasn't super random, your lack of thinking and looking would gain you no advantage towards knowing what the next cards are in the deck, because you didn't keep track of them while shuffling. Of course you probably have to shuffle it so many times anyway.
The other thing as to why people shuffle like crap is because they don't want to shuffle. They want to play. I've had fits of rage when I have to shuffle my deck and I keep on getting the same crap over and over, and it is annoying. Not random at all, until I discovered mash shuffling with sleeves. Before I didn't use sleeves and did the hand over hand shuffle technique, which sucked, especially if you have bent cards, so to fix that, I alter the starting condition of the shuffle, so that the end result would be different than before. I would move cards around without looking at the cards, and do the pile shuffle thing. Not as random, but you can't expect people, especially kids, which this game is aimed at, to be master shufflers who could do it in a short amount of time. Oh, that was when I was playing MTG all day every day, before I decided to split my time and cash on 3 TCG's. It doesn't matter now, sleeves + mash shuffling = win. Much quicker, and I don't have to deal with pile shuffling anymore, and it is more random, well not totally random, because 100% random is impossible. So long as it is 70% random, it is good enough for me. I am not going to shuffle till I am blue in the face just to achieve the 100% randomness, but then again, I shouldn't be thinking about getting that hard to get card order through random shuffling, because when shuffling, you don't think.
I do have one problem though, when shuffling MTG intro packs, yugioh structure decks, or Pokemon theme decks, I tend to have the urge to reshuffle when the foil/holo/ultra rare is the top or bottom card, and that is when I shuffle the deck and not play, because I felt like shuffling out of boredom, even though I know what I get is what I get. It maybe has to do with the way I cut the deck because foils/holos usually bend, and they mostly end up as the bottom or top card, which is kind of a bummer.