Since a .net exception is a .NET object like any other, it gets stored on the GC heap when you (or some code you call) calls new XXException().
This means that if you have a memory dump of a process you can dump out all the recent exceptions that have occurred, or rather all exceptions that have not yet been garbage collected, which will give you a good feel for what exceptions occurred recently.
Doing this is pretty easy if you have sos loaded (.loadby sos mscorwks) in windbg
0:015> !dumpheap -type Exception
------------------------------
Heap 0
Address MT Size
02ea6b0c 79330a80 72
02ea75f0 7930eab4 76
?
06f57aa4 7930eab4 & ...
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