1) Where is the GPL not a contract?
In order for a binding document to not be a contract, it has to be deficient in one or more of the required elements. In law derived from English common law, a contract requires a true agreement between competent parties with an exchange of consideration. This, however is true (as far as I've been able to research it) only in the US, Canada (other than Quebec), England (but not Scotland. I have no information on the rest of the UK and the Channel Islands, the British West Indies, Gibraltar, the Falklands...), Australia and New Zealand. It is only in these countries that the issue has any potential significance.

2) Where does it matter if the GPL is a contract?
In order for it to matter, there has to be some legal advantage to one of the two possibilities. In the US, cpntract disputes are handled in state court, while infringement is handled in Federal Court. Also the different states have subtly different contract law. Finally, with infringement comes the possibility of statutory damages (no need to prove actual damages) and the presumption of irreparable injury when seeking an injunction. While Australia, Canada and the UK (to some extent) have federal systems, their copyright laws are sufficiently different from those of the US, that the contract question doesn't appear to make that much difference.

3) Is the GPL enforceable in the US regardless
The answer is fairly clearly yes. If the copyright holder explicitly revokes the license for cause, then, after some period required for fairness, any continued reliance on the license would be infringement. This is true whether the license is a pure license, an agreement without consideration, or a contract. The GPL could be improved in this area by explicit language about rescinding the license. Such language shouldn't affect the GPL's status as a pure license, to whatever extent it exists. However, no court would hold that absent such language, the copyright holder would have no right to rescind the license for violation of its provisions.

4) If the GPL is a pure license, does it escape contract law?
Almost certainly not. Contract law applies to agreements that aren't contracts; it just doesn't have as much to say. It would certainly be used to interpret the meaning of the GPL, since the copyright act provides that nonexclusive licenses are regulated by state law (other than possibly the question of infringement).

5) Are all violations of the GPL infringement?
Probably not. If the GPL was a contract, then any provisions that were considered covenants of the agreement, as opposed to conditions of the license , would not be infringement, and the remedy would be an action for breach of contract in state court. There is no reason that the situation should be different if the GPL is not a contract. The general rule is that conditions are bound to the scope of the license. A provision that allowed for serial rights but not movie rights would be a condition. A provision for payment of royalties would generally be a covenant. It is possible that the GPL could be modified so that the source distribution requirement was a condition, but it is not clear that this is now the case, since the source doesn't have to be distributed with the derivative work. A condition usually needs to be something that is always required without which distribution is not allowed. Something that happens separately or later or somewhere else is suspect. If, for instance, a royalty agreement required a receipt for payment in full to distribute, it might rise to the level of a condition.

6) If the GPL is a pure license and it has provisions that are covenants, is there a remedy for violations of them?
My feeling is that the answer is yes, but at this point it's time to say IANAL. Ask one. Better yet, ask several.