When we are talking about receiving a transaction, presumably that means that someone sends some bitcoins to an address generated by my client.

What if I give out an address before I've downloaded all the blocks and someone sends something to it? Why would that be bad, I'll just see the balance change in my client once it catches up to the block with the transaction in it, surely?

Why do I have to wait until I get all the blocks before someone can send some bitcoins? What if I'm just one block behind?

Sure, I understand it for outgoing transactions, otherwise my balance could be wrong.

What about incoming transactions?

Well, that explains it.

It just made me concerned because I was backing up my wallet.dat, but then I could see it had changed since the backup.

wallet.dat seems like a counter-intuitive place to keep information on the latest blocks.

I've noticed that wallet.dat changes even though I've not generated new addresses, carried out any transactions, etc.

Under what circumstances does wallet.dat change?

No response from the OP probably means that the BTC have turned up now. 

On https://en.bitcoin.it/wiki/Using_Bitcoin it says that I "must get all of the blocks in the chain before sending/receiving transactions".

Can anyone tell me why this is the case?