Find "cfprm.pdf" on Freescale's site, download and read the "Exception Processing" chapter.
Read Section 3.7 in the MCF5275 Reference Manual. It is very good and has a huge section describing all the exceptions. If you then search the PDF document for "access error" you'll get 14 matches, many of which list what can cause this exception.
"Illegal instructions" are obvious. The CPU started fetching from where there aren't legal instructions. This is detailed in the Reference Manual too.
But you don't want to know what these are, you want someone to tell you how to make them go away.
Mark already did that. His link gives an excellent tutorial for debugging all sorts of problems like this.
Simply put, you use the debugger, then inspect the stack and memory to see how the CPU got to where it crashed.
Another old-fashioned but workable method is to mix single-stepping through the code with putting breakpoints "ahead" in the code and then seeing if it gets there or crashes before that point. Then you try again with different breakpoints, zeroing in on where it is failing.When you find the failing instructions it should be obvious.
The VERY old fashioned way to do this is to put print statements (or code to flash a LED) in the code, recompile, reload and so on, again zeroing in on where it is crashing. Sometimes these bugs can take weeks to find in complex code.
Another problem is getting an interrupt the CPU isn't set up to handle. So make sure you have "dummy interrupt handlers" for all possible interrupts, and put a breakpoint on that so it will let you know when this happens.
If you follow all of Mark's instructions and are still having problems you can say how far you got (in those instructions), what was on the stack, what is in the registers and where it was in your code (provide short extracts).
Tom