The Trace?

In the seventh book, it's stated that the Ministry know when underage witches and wizards perform magic because they have a trace on them, but in Chamber of Secrets, Dobby does a spell and Harry gets blamed for it because there was nobody else there, so do you just have to perform magic close to somebody who has the trace to set it off? But then, in Order of The Phoenix, Tonks is helping Harry pack his things and uses a spell, and there is no owl warning Harry for use of underage magic. And, how would that work in an all magic family, like Ron's, where adult wizards use magic all the time? Any theories?

Can you say, "T.I.R.A.D.E.?"

Yes, I believe T.I.R.A.D.E. is the answer

Herms, great work on pointing out ANOTHER TIRADE- worthy contradiction in DH. If one assumes the Trace is on the actual person- which would explain why Tonks can use magic around Harry and Harry doesn't get in trouble for it- than why can Dobby use magic and have Harry get blamed for it?
Conversely, if the Trace deals with general proximity more than one the actual person, like one has to assume considering the pudding scenario with Dobby- than why does Tonks' use of magic (or even Dumbledore's) not get him in trouble, despite the fact that Order-related visits are definitely under the rader as far as the Ministry. And, as Herms brings up, what about numerous magical users- both over age and under age, living in close proximity?

And with the Weasleys- what do they do with Fred and George? Do you really believed they didn't use ANY magic over the summer holidays before they were seventeen? It's implied they got at least one warning... but they certainly weren't expelled. Harry was accused of using magic ONCE, and was already threatened with expulsion.

definitely true with the whole tonks/dobby thing. but as far as the weasleys, it said in the book i think that the parents were responsible for monitoring the kids

yes and when mr.weasly blew open the fireplace in the 4th book
and when the guard came to get harry in the 5th. they used magic both times and nothin happened.

but see this time mr. weasley had to connect the flu network to the dursleys home so a possible explanation there is they (the ministry) knew that an overage wizard would be there.

Yea but remember at the time Harry was not liked by the ministry and that's why he was threatened with expullsion.