All 3 of these have been on the market for a while. The first and the last are the two that catch my eye most from the descriptions and what's shown in the photo's. Personally I'd prefer the manual and the price of the private one isn't outrageous.

I don't think there are any specific 325 issues to look for so its the usual M54 stuff such as cooling system, cam and crank sensors, ABS/TC sensors, etc. As per Andy's comment, any issues with the cooling (other than preventative maintenance), especially any mention of the head gasket, either now or in the history, then walk away.

Convertible specific stuff to look for should be obvious and focus on the hood, electric motors, etc. for same and the rubber seals, etc. If there are any issues with these make sure to get a significant wedge of flexibility on the price as these are expensive replacements or repairs if needed. A hood that leaks or doesn't seal properly will soon turn a nice car in to a mushroom farm. Heated seats are a very desirable option on a convertible and see if there is a wind deflector in the car, makes a big difference to comfort on the move. The deflectors aren't too pricey but its nice if its there.

My sister had a '05 330Ci conv for 8 years and loved it (chopped it against a 420d last year). Just referring back to the comment above about the private sale car, to put in context, when the main dealer retailed her p/ex 330 it was up for around 12k and sold very quickly.

My first convertible was a 45k miles e30 320i that I bought back in 2001 and kept for a couple of years. It probably provided more smiles per mile than any other car I've had.