I agree with Andy for the most part. My rule has always been that even if the image is amazing, if the audio is bad the audience will hate what they are watching and won't know why (it will be because they have to spend extra effort to understand the audio they are hearing).
However IMHO for strictly archival and transcription purposes, cheap quick low-quality cellphone/cheap camcorder stuff CAN sometimes work.
Also per what Isarra said, if audio is being amplified in any way, it's best to plug your video camera/audio recorder into that source directly, or
indirectly:
Sometimes though, audience members will ask questions, and those might not be recorded. Again, having a professional there helps with this.