When changing clip speed via properties, there is audio glitching where the clips start and end, which shows up in the final export

I would be interesting if someone could do an A/B comparison with some other tools. The problem with slowing down audio is that you are effectively reducing the sample rate. For example, if your audio is 48Khz, but you slow it down to 0.5x, then Shotcut only has 24Khz to work with. The quality will seem lower for sure.

You should try the Time Remap Filter sometime. This is the most advanced form of speed change that Shotcut offers. It is a bit of a “head change” for many people. But if you master it, it provides all the detailed control you could want - including anchoring source frame numbers to output frame numbers.