First off, the E46 M3 convertible was built (model years) from 2001-2006 and, as a former owner of an 02 M3 vert, a great value for the performance and style. Things to be careful of are the rod bearing recall that affected the S54 engine from 2001 - early 2003 (although most issues were in engines build during the last quarter of 2001 and early 02 IIRC). Check service history to make sure the work was done if you are looking in this date range. Most 03s were out of the woods for the problems but were still covered with the extra 100k mile engine warranty (most of which will have expired by now anyway.) Rear subframe was an issue with coupes; window regulators are weak in all E46s; wouldn't buy a high mile SMG car; check the Ti shadow trim on the interior for cracking; ...
All E46 M3s were updated with small modifications like LED tail lamps and a new AC system starting with build dates around 01/03 - 02/03. Another change for all 03 models was the addition of a strut tower brace, very important to reduce the flex in the vert chassis (although you can add one yourself for about $200.)
No big 'vert-specific issues that I am aware of, just make sure that the top has been well maintained, works properly and doesn't leak - no specific issues that I know of but some people had top alignment issues over time.
As others said, go look around the E46 M forum or on one of the other competing sites. Good luck, they are great open top cars for the money.