Hi Coachalla and welcome to the RH community.
I know this is outside of your control but copying and pasting images into Word and then expecting them to be clear when importing them into RH is not a good idea. It sounds from what you say that the images have been added in a variety of different ways. Do you have access to the original images? If so, I'd start by readding them in your RH project. There is a topic here that explains best practice. If you haven't, maybe recapture them from the WOrd document and add them to the project.
One further thought. You haven't said whether you are using the RH for Word or RH HTML application. If the later, you may want to save the images into a different file format. JPG or GIF will significantly reduce the file size.
Read the RoboColum(n) for mutterings on RoboHelp, Technical Communication Suite and technical communication.
I can't imagine how they got to version 8 and didn't consider that people might, A) create help systems by importing existing manuals from Word, B) send those documents back to print using single sourcing, and C) maybe those screenshots should look as good going back as they did coming in, not look illegible.
I recommended RoboHelp to my client, got them to spend money on it, and now the documents look like crap. I realize the fault may lie with the Microsoft API and all the oddities that may exist in how Word stores images, but since they went to XML, in theory, how bad can it be?
Does someone from Adobe (or any of the chain of companies they bought since RoboHelp was released) have a solution to this?
First this is a user to user forum and whilst some of the folks at Adobe put their own time into answering posts, it is not an official support channel so asking Adobe to respond has little chance.
Of course the flow you describe has been considered and normally it works just fine. I for one have done it many times. Usually any problems are down to the source. The topic below is a few years old but I believe it is still valid.
That will not put anything right but it will show how different methods affect things. If you send me a project with one topic created from one of these Word imports, I will take a look. Keep it small and send it via http://cutesendit.com with a link to this post. You can get an address via my site.
It sounds like you are generating a CHM but you don't say that specifically.
See www.grainge.org for RoboHelp and Authoring tips