I have a 65g goldfish tank which is heavily stocked (borderline overstocked, but they spend the summer in the pond). It currently has an AC110, which I am positive is not wokring properly (water flows over the foam/media, not through it, not nearly as good as it used to be when I got it 2-3 yrs ago).

Can anyone advise a good filter for a tank with messy fish? (only room for one filter due to outlets available)

It needs to handle a lot of waste (ever see how much poo an 10" goldfish can produce?)
It needs to be easy to clean (at least the foam part for the wastes)
It needs to be fairly quite (it is in a bedroom with a light sleeper).

A few other sites seem to suggest Rena and Eheim models - any advice/suggestions?

I would go with a Rena xp3, very reliable fairly cheep and lots of filter options!

Rena XP3s are awesome for keeping filthy fish, I don't know I'd put it in a bedroom with a light sleeper tho. They can be noisy. If an air bubble gets caught in it anywhere it makes fun burbling sounds till it works it out. One of mine occasionally makes a wooshing noise as well. It doesn't bother me, but I can fall asleep near anywhere. Another thing to note, the XP series are all gravity fed, so you'd need to keep the filter lower than the tank.

Hardcore overkill, but the Pondmaster 1500 is also dead silent when completely submerged, you'd just need to point the outlet into the water instead of using the fountainheads. I have an 80ish gallon kiddy pool set up with 4 near adult red ear sliders in it (Major filth magnets) and it keeps them clean. If you have a spare pump you could build your own, too for that matter.

Another filter I've been impressed with recently too is the Hagen Liberty. I got a few of them really cheap and they work really well for as tiny as they are. I've only tested them on 30s but they are rated to 200 gallons.