One annoyance is that it often feels like "./configure ..." takes longer to run than the actual "make".
But my main annoyance derives from that fact that most projects I build from source which use autotools don't build cleanly on anything but Linux x86/amd64. I spend a lot of time playing with non-Linux and/or non-x86 Unix systems, or using vendor compilers instead of gcc -- primarily Solaris (both x86 and SPARC), Linux on POWER, and AIX on POWER. Current versions of IBM's compilers, Sun (err...Oracle's) compilers, etc. Run the configure script, let it slowly probe all the little corners of whatever it's probing, and sometimes I'm lucky enough that it completes successfully and claims to understand the environment it's in. Then run make (or, as is often required, GNU make), and hit build errors very quickly.
Which makes me think... why did I just sit through that long "configure" script run, and why did the developer bother messing with autotools, if this project isn't even going to bother targeting anything but Linux with the GNU toolchain to build it? If you're not concerned about portability, it seems a relatively simple Makefile would be an easier and faster approach. Why foist the [insert your favorite colorful descriptor here, depending on your personal feelings] autoconf system on builders of your project?