Apparently I need to Reset blockchain and transactions to resync my wallet, but I've been advised to upgrade to the latest version of Multibit before doing anything. Does anyone know if it's safe to do this in Multibit HD, or have I got to download the latest version of Multibit Classic? Will I need to extract my keys or can I use the current .wallet file on my mac?
Multibit HD does not allow the importing of keys so you have to sweep them. Additionally, Multibit HD is rather unstable so I don't really recommend you going to that path.
You should download the latest version of Multibit Classic and that makes everything much easier. Its advised to transfer your Bitcoins to another wallet, I recommend Electrum. The easier way is obviously to extract your private keys and sweep it into Electrum. Look at my post:
https://bitcointalk.org/index.php?topic=1959806.msg19477410#msg19477410.