Emacs uses a shell to run the compilation command, but specifies the option for a noninteractive shell. This means, in particular, that the shell should start with no prompt. If you find your usual shell prompt making an unsightly appearance in the *compilation* buffer, it means you have made a mistake in your shell's init file by setting the prompt unconditionally. (This init file's name may be .bashrc, .profile, .cshrc, .shrc, or various other things, depending on the shell you use.) The shell init file should set the prompt only if there already is a prompt. In csh, here is how to do it:
if ($?prompt) set prompt = … |
And here's how to do it in bash:
if [ "${PS1+set}" = set ] then PS1=… fi |
There may well be other things that your shell's init file ought to do only for an interactive shell. You can use the same method to conditionalize them.
The MS-DOS "operating system" does not support asynchronous subprocesses; to work around this lack, M-x compile runs the compilation command synchronously on MS-DOS. As a consequence, you must wait until the command finishes before you can do anything else in Emacs. Appendix E.