When you say you can see the brush marks, do you mean that they're actually irregularly surfaced? I mean - are we talking just a visual effect or an actual difference in the depth of the paint?
If the latter, do a skim coat with lightweight joint compound and when it dries, either lightly sand OR smooth with a large, slightly damp sponge, then apply primer.
As for your own brush strokes - orient the roller so the roller bar leads your motion. If you're moving right, put the bar on the right. If you're moving left, put the bar on the left. The most pressure will be on the roller bar side, so keeping that side on the "front" of your motion will mean the lighter touch side (the back) will smooth out the uneven strokes as you pass over it again.
Now if its not a real issue with texture, just that your seams are obvious - then just prime it again with a good HEAVY primer, using the proper brush techniques, and you'll be fine. :)
In my experience in painting my own house over 50 years I only sand when necessary, that is when the paint is loose, or, the surface is glossy. I just repainted some trim on my house that has Semi-Gloss paint. And, I sanded it first. I did this to improve the adhesion of the new paint. But, most of my house has flat paint, and I never sand it unless I'm blending an area where I had to remove some loose paint.
Update, 11/14/13: I re-read this today, including all the posts. It's interesting to see the different opinions about this subject. No wonder you had a question after searching the net.
My take on this is that if you are a perfectionist, you'll decide to remove it all. If you're just painting to resell, you'll scrape the loose off and paint. If you're going to keep it and use common sense, you'll scrape, sand where you need to feather edges for aesthetics, and paint. That's assuming its flat paint. For glossy finishes, you really better sand it to ensure the new paint sticks permanently. Incidentally, I always clean before scraping with Tide and bleach solution and brush hooked to expandable pole, and sometimes with a power washer to quickly knock off loose paint. Also, after sanding, I blow off the sanded surfaces with a blower, or brush it with a big paintbrush, or wipe it with rubbing alcohol or water.
Recently I used the tool below to "sand" the loose paint off my deck before repainting and was very impressed with it's efficiency. I like how it gets down into the cracks between the paint and wood and smooths out the ridges, as well as how quickly its use is. You might want to pick one of these up and give it a try.
Finally, one last tip. You can always do a test by painting a small area, waiting several days, then trying to scrape it off. That's how I learned how important sanding is for glossy paint.
Best Answer
It looks like patches to the sheetrock or maybe wet spots and the rock is not in good shape. You should evaluate if the sheetrock is not solid it should be cut out and replaced. I usually use green board for repairs in bathrooms.(Green board is water resistant sheetrock). I would scrape and see if the paint is well bonded if it is well bonded fill the low spots with topping mud then prime for best results.