you have a number of good answers. the wildest problems i've had to chase come from stack corruption issues like barry mentioned. i've seen stuff happen with the project's "Memory sizes" section on the linker page. i might be superstitious but it seemed like larger wasn't necessarily better. you might consider using the enhanced memory manager FastMM4--it's free & very helpful.
http://sourceforge.net/projects/fastmm/
i've used it with d7 and found some access to stale pointers and other evil things.
you may also wish to create a way to track valid objects and or instrument the code in other ways to have the code checking itself as it works.
when i'm seeing access to addresses like 0x00001000 or less, i think of access to a nil pointer. myStringList:=nil; myStringList.Clear;
when i'm seeing access to other addresses with much larger numbers, i think of stale pointers.
when things are strangely unstable & stack traces are proving to be nonsense and/or wildly varying, i know i have stack issues. one time it's in Controls.pas; next time it's in mmsys.pas, etc.
using the wrong calling convention to a DLL can really mess up your stack as well. this is because of the parameter passing/releasing when calling/returning from the DLL.
MadExcept will be helpful in finding the source of this, even if it shows nonsense...you'll win either way because you'll know where the problem is occurring or you'll know you have a stack issue.
is there any testing framework you can put on it to exercise it? i've found that to be very powerful because it makes it entirely repeatable.
i've fixed some pretty ugly problems this way.