Yes, it is common for toddlers to cry when things are not in order. Why?
First off, at that age, kids like consistency because it offers a sense of security. Knowing things are always in their place means that other, more important things will also always be in their place - like mommy and daddy will always come home, food will always be on the table, etc. They cry when they think it should be one way and it isn't, because their sense of security is lessened.
Second, because they are constantly learning new things, it is easier on them if things they've already 'learned' are constant. Parenting Magazine has a good article on the subject of repetition, and things being in their place is a form of (long-term) repetition. When things are not constant, it stresses them out, as something they thought they'd learned proved to be false - something still a problem for adults often.
Third, in a related element, things being always the same is how they learn how things 'should' be - whether it is learning that mommy loves them, that "B" says "Buh", or that a table always has four chairs. It's in particular how they learn behavior and social protocols; mommy always does something, so they learn that is what they should do. Hence crying when, for example, sister doesn't sit down when she should - because they think that's the rule and don't understand why it isn't.
Fourth, toddlers haven't learned about gradients yet. Everything is black or white - you should do something or you shouldn't. The concept of "pick your battles" is alien to them. More, though, this means that even very minor things can be 'huge problems', which leads to crying.
Finally, toddlers like to have a sense of control over their environment. They're small, and mostly have to do what they're told, so they like to exert control over what they can. Some of the crying over things being out of place is trying to exert this control.
Our approach with our soon to be three year old son is that every time he has a 'problem' to discuss whether it is a 'big problem' or a 'little problem'. His little brother not doing something he should is a 'little problem', unless he's biting or hurting him, in which case it is a 'big problem'. Spilling his milk or even breaking a cup on accident is a 'little problem'. Running towards the street is a 'big problem'. Etc. Making it clear that things that truly threaten safety are big problems, and most other things are little problems, has helped him learn not to sweat small things - he still has to help clean up the milk, but he's not in trouble and there aren't serious consequences.
Other things, like using the proper bowls or sitting in the right spot, we largely deal with by asking him what he wants. It gives him a sense of control, and also avoids some of the complaints over things being out of place or incorrect, since he can tell us what the right rule is. Some of these rules are undoubtedly patterns that he noticed that we don't - so we let him figure it out and tell us when it doesn't make much real difference.
Otherwise, though, we just talk to him about what's bothering him and try to explain the right way to go about telling us something's out of place. Door should be closed? Okay, go close it. Mommy not doing something right? Ask her politely to do it the other way. Also, accept 'no' - which doesn't go terribly well still, but it's a (long) work in progress.