Be careful here, a few things of note from my experience...
When it is shorted you will read 0 (zero) or very very close to it.
When there is a circuit in the path of any kind you could get continuity with some amount of resistance that isn't an open, but isn't a short. Be careful to read if it is 10's or 100's or 1000's or 1,000,000's of ohms or whatever. If you're not careful you could read 1 megohm as 1 ohm if you don't understand how your meter shows the multiplier.
When you are looking at a true open most meters will read either OL for Over Limit, or as in Virtues case his meter is showing a capital "I" for Infinite (by the meters scale which usually means greater than 10 megohm).
There is a good bit more, like what going across a capacitor looks like (short climbing in resistance to an open) or multiple resistance paths through a parallel circuit etc etc.
It is easy to think you have a problem when you don't if the evaluation of the reading and why you may be getting it is misdiagnosed.
Just my 2 cents.