Well done for getting your hyper pooch 'fixed' Murt! (Didn't see River Cottage, am guessing it ended up as spaghetti and meatballs *ahem*? Eek!)
We've two mutts, one from the doggie dustbin aka the pound and the other from a shelter. We didn't know what we were getting at the time and one of the mutts (Spud, the one from the shelter) is totally hyper and loves to play, play, play.
A couple of years after getting Spud we were visiting a cheetah park in South Africa (not with Spud!) and the keeper was pointing out the big cats' long legs, big rib cage, rangy build all of which means they were built for running ... at which meself and himself went 'Ah ha!' 'cos that pretty much described Spud the Mad.
Penny, who arrived later, is a barrel shaped thing who's main goal in life is getting her belly rubbed. She's not half as interested in running about and chasing rubber bones.
What I'm getting at is if you take in a mutt and know what to look for (unlike us!) you can have a fair idea of what they're going to be like. That and the pound/rescue shelter should be able to tell you a bit about that particular dog's temperment as they've been looking after it for a while.
You'll also be able to figure out (usually!) some of the 'main ingredients' of the mutt e.g. is is mostly GSD, terrier, collie, etc.? And from that you should be able to make a stab at judging its capabilities and temperment (e.g. terrier = feisty, lively, GSD = loyal, intelligent, bit of a coward, collie = v. intelligent)
Of course then there's the nature versus nurture debate - a dog who is badly trained or getting the wrong signals from its 'pack' (that's you and your family) will always be a handful. And vice versa. ('The Dog Whisperer' by Jan Fennel is a good insight into this side of things). Training and how the dog is treated will have as much of an effect on a dog's behaviour as its breeding.
Anyhoo, here are my mutts:
Penny (before she was 'sprung' from the pound - she spent five days in that cage, it was one of the 'good' pounds. She should have been killed on the first day because she was a surrender. She was surrendered apparenlty because her previous owners lived in a flat where they weren't allowed pets and Penny was discovered.):
http://www.muchos.co.uk/members/spud/penny small.JPG
Spud:
[broken link removed]
Spud and Penny (after Penny was sprung from the pound):