Hi Dave,
Your question is very, very broad.
Processing astro images does require a bit of a rethink as the data you're working with is quite different from terrestrial daytime images.
Effectively processing astro images is all about making the most of very faint signals and controlling noise. The two are always at odds and they're an art more than a science.
Issue #1 to get your head around, would be clipping. Histograms are a tool to help you avoid white and black clipping when you're stretching your signal, so getting familiar with them is highly recommended (unless you're ready to leave those archaic ways behind and use StarTools of course
).
Issue #2 is knowing when an image is done and getting it right the first time, so you don't keep running around in circles 'overcooking' the image in the process.
Issue #3 is knowing why an image looks like it does before you have even touched it. Understanding why the color is off, what that black blob is doing there, why those stars are elongated or discolored etc., will help you pick the right tools and lets you troubleshoot effectively. E.g. if you don't understand the problem, how can you effectively and consistently solve it?
There are heaps more things to think about, but once an absolute beginner myself, these are the things that helped me most.
Hope this helps!
Cheers,