Does Primer Have to be Perfect on an Interior Wall?

For interior wall painting over old paint, you really should first hit it with a primer/sealer.  It will give you a chemical barrier to prevent the old color from messing up the new color.  However, don't worry about it looking perfect while applying or after it dries.  You just need a thin layer for it to do its job - even a see-through layer or one with what appears to have thicker/darker stripes will do.  Below is a typical ugly look of primer applied with a roller:

Compared to paint, it will go on very thin.  If you go a comfortable speed, by the time you come back to do your next section with a little overlap, rather than it being a good wet joining with the previous section, it primes over with a true second coat at the overlap. In turn, you will see it look like a better coated stripe amidst two big thin layers. Don't worry, it won't show once you paint over it.  Below is the same wall after painting:

The paint looks great - the only imperfections are actually due to the mud/tape job done when the house was built. Otherwise, there is no sign of how the primer appeared before.

When getting paint, get at least a mid-grade paint or better.  It will be more viscous, putting more paint on at once without running saving you from having to do a second coat.  Also, it stays wet long enough to have a sufficiently wet edge even at a casual pace so you don't get stripes. 

"Cut in" first, but just enough to do your current section.  If you cut in and let it dry, you'll see the "second coat" effect.  Don't worry about taping the ceiling, trim, and baseboards.  Just use a sash brush to cut in and you'll develop a twist technique naturally that allows you to lay it perfectly.  If you get any on the baseboard, just use a damp paper towel and wipe it off. Running a bead of white caulk after it all dries can clean up any oopses, too.

When rolling, lay out a W pattern and then roll it in.  Don't ever try to milk out every last drop in your paint tray - keep filling it up when it get's less than an 1/8th inch deep.  Otherwise, when you roll, it will not lay down wet paint and is likely to pull up paint from your prior stroke.

If you do see where you didn't sufficiently coat a spot within 20 minutes of painting, you can load up your roller again and touch it up. You may want to do a line from top to bottom. You will see where you touched it up for a couple of hours since it is wetter than the first coat and catches the light differently, but once it fully cures after 4 hours or more, it will be very hard to tell.  In turn, you should be able to achieve a paint job with only one prime coat and one paint coat - with mid to high grade paint, that is.

Last - don't paint over wallpaper.  It's just embarrassing.  They make a tool and have a glue solvent that will get it down for a professional look.

Remember - it's just paint!

-Sean