Here are some things to look for:
Sensor: The bigger the better but also the more expensive. With a bigger sensor, that megapixel analogie I used earlier may change from a 75g tank to a 500g tank in reference to how many megapixels are too many. You probably won't get a larger sensor than the camera noted above, so don't worry too much about this.
ISO speeds: This lets you get away with "better" shots in darker conditions. High ISO speeds show film grain (techno-colored dots all over the image). A larger sensor will typically fair better with higher ISO
Aperture: A lower number is a better number. f/2.8 is good, f/5.6 isn't very good. If a camera says the aperture is f/2.8-f/5.6, that means zoomed all the way out (5mm) you can use f/2.8...zoomed all the way in (20mm) f/5.6 is the best you can do (so zoomed all the way in probably won't be a good choice on a reef tank). I realize you don't know what those numbers really mean but just remember lower is better. Finding a non DSLR camera like this will be...difficult at best. Heck most of the DSLR lenses are plagued with this physics problem.
Auto focus: Just about every camera has auto focus so this is a tough call. Other than goggling it, it would be hard to tell if the AF is decant or not so much.
Manual focus: I would try to find a camera that can do this.
Manual mode: You don't want a fully automatic camera for a reef tank. There are too many variables. Try to find a camera that has (Nikon) A, S, P, M as settings or (Canon) Av, Tv, P, M. With a little old fashioned knowledge, these will give you some control over what the camera is doing.
Uncompressed format: The basic term for this is "RAW". This would be as opposed to compressed formats such as "JPEG" or "TIFF". The camera above could only shoot JPEG, try to find one that shoots RAW as well.
Tripod: That's right, I said it.
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Okay that is the basics to look for as I see it. I am a Canon man and a little bias, but it is what I know and understand. Here are some Canon cameras that could do well with a reef IMO.
Canon Powershot G10
This one may be a bit out of your price range, but unlike the DSLR there aren't $1000s worth of lenses to buy on top. A DSLR is going to be the best option for a reef tank, but I think this little gem is next in line. You could pinch some pennys by looking for a used G9 or G8 or heck even a G7, now a great-grandpa, is still better than most others.
Canon Powershot SX10 IS
One of our members recently bought this camera and was less than thrilled. If you take the time to understand the camera I am confident that it is capable.
Canon Powershot SX1 IS
Or, if you really like Movies, this version is similar but instead of a rare for Canon CCD sensor, it has the traditional CMOS and can also shoot HD movies.
Canon EOS-1Ds Mk III
Haha just kidding.
Canon PowerShot A650 IS
This one seems to cover all the bases.
The lack of a RAW file format is unfortunate but common with P&S cameras.
