If Emacs executes an illegal instruction, or dies with an operating system error message that indicates a problem in the program (as opposed to something like "disk full"), then it is certainly a bug.
If Emacs updates the display in a way that does not correspond to what is in the buffer, then it is certainly a bug. If a command seems to do the wrong thing but the problem corrects itself if you type C-l, it is a case of incorrect display updating.
Taking forever to complete a command can be a bug, but you must make certain that it was really Emacs's fault. Some commands simply take a long time. Type C-g and then C-h l to see whether the input Emacs received was what you intended to type; if the input was such that you know it should have been processed quickly, report a bug. If you don't know whether the command should take a long time, find out by looking in the manual or by asking for assistance.
If a command you are familiar with causes an Emacs error message in a case where its usual definition ought to be reasonable, it is probably a bug.
If a command does the wrong thing, that is a bug. But be sure you know for certain what it ought to have done. If you aren't familiar with the command, or don't know for certain how the command is supposed to work, then it might actually be working right. Rather than jumping to conclusions, show the problem to someone who knows for certain.
Finally, a command's intended definition may not be best for editing with. This is a very important sort of problem, but it is also a matter of judgment. Also, it is easy to come to such a conclusion out of ignorance of some of the existing features. It is probably best not to complain about such a problem until you have checked the documentation in the usual ways, feel confident that you understand it, and know for certain that what you want is not available. If you are not sure what the command is supposed to do after a careful reading of the manual, check the index and glossary for any terms that may be unclear.
If after careful rereading of the manual you still do not understand what the command should do, that indicates a bug in the manual, which you should report. The manual's job is to make everything clear to people who are not Emacs experts--including you. It is just as important to report documentation bugs as program bugs.
If the on-line documentation string of a function or variable disagrees with the manual, one of them must be wrong; that is a bug.