What is the best way to convert a video with 29.97 frames/sec. (interlaced) to 23.98 frames/sec. (progressive) without resulting in interlacing artifacts (jagged edges on movement)? Preferably, using common software like Compressor, Final Cut Pro 7 or After Effects.
You can use Compressor. You'll just have to tweak the frame controls until you're satisfied with the results.
There's no magic bullet fix or 1, 2, 3 process. It depends on the originating camera, codec, type of footage, and what you're willing to accept. The image will likely be a bit softer as you're either combining fields or you're throwing one way and interpolating between the two.
I would get a sample file (30 seconds long or so) and use that to test out several different settings. Assuming you have a lot to do, find the setting you like best based off your sample clip and then run all your footage through in a batch overnight. Depending on the settings you can choose it can take close to realtime or up to 5 to 10 times realtime (based largely on what setting you choose for "Motion Estimation"). Remember this process is very computationally heavy. So leave yourself plenty of time to test and transcode.