Our spare bedroom has one red wall (3 white) and a red 4″ moulding running round the white walls.

Anyway. I have undercoated the red wall white, and applied 2 coats of the new colour (yellow). There are some small red dots coming through, they look like measles, and I don’t know what to do to get rid of them. Any ideas?

Your new paint will be reacting with the old paint. Happens a lot. You can get some sealer to paint over the old, or get some oil based undercoat, and go over it with that.
What usually happens is you put a coat of emulsion on a ceiling, then, 10 minutes later, you start getting bubbles showing. If left, these can sometimes shrink back, but more usually they get pulled off as you put a second coat on, as they are only just forming, so are easily pulled off by the roller.

There are also some additives that you can add to your emulsion to stop this happening, but for a one-off they are quite expensive (they dont sell a small pot of it).
Some info here:
http://www.albany.ie/index.php?option=com_content&task=view&id=88

thanks. will give that a try.