In general, you just need to take a few extra precautions.
- Situate each member in an room with minimal distractions and isolated from noises. If possible, go somewhere without pets - everyone loves pets, but everyone also knows that they have no sense of privacy, will make noise when they verily well feel, and in the case of dogs, their bladders know not the meaning of "Do not disturb". They're just doing what they do, but it's just an interruption that can maybe be avoided
- Likewise, avoid being too close to a window especially during the day - the sunlight may provide some really pretty back-lighting, but auto-color correction on a lot of web cameras will be constantly fighting with the sunlight should a cloud pass, shadows rise/fall, and so on
- A wired connection is strongly recommended just to remove the variable of WiFi interference kicking up unexpectedly
- Headsets are strongly recommended, or at least a quality microphone with the speaker having an earbud to isolate any possible feedback. Wired strongly preferred
- In a similar vein, fixed apparatuses are preferred (i.e., no in-line microphones like what you get with cell-phones). They tend to brush against fabric and make awful noises, or twist or turn
- Take some time prior to the actual recording to just sound-check and also get used to the tiny delays that often occur with interviews. 10-20 minutes is often good enough just as a warm up
- Make sure that all participants are used to speaking on video and through mics. There is a bit of an art to doing it right with video chat, avoiding either being too loud/blaring or too soft
- Finally, test whatever screen recording software you're using multiple times before the call and test it in a real call situation to ensure that there are no audio goofs. This can be part of the 10-20 minute test. It goes without saying, but you'll probably want to use a moderately modern machine that won't chug when recording, and also have enough space to store the recording
These are what we used for my workplace when we did Skype interviews and needed to record them for review later on.