I noticed a 2417 byte transaction with a 2.7 BTC transaction fee. Is there any rational explanation for this, or was it perhaps a mistake?
What's also possible is that someone mistakenly swapped the sending amount and the transaction fee amount. I almost did that with the bockchain.info wallet but luckily noticed it in the confirmation screen.
In this case, he could have intended a fee of 0.02314796 BTC and tried to send 2.7 BTC to the address. The other 65+ BTC could be just change.
There certainly is a rationale explanation- if you are manually constructing your own transactions i.e. you are writing your own code to create bitcoin transactions its pretty easy to do this by accident.
The reason this is so easy is because there is no explicit 'transaction fee' output, rather transaction fee = total inputs - total outputs. Hence it is pretty easy to accidentally forget to e.g. send. the remainder back to yourself or to miscalculate the remainder.
I did this once when I was testing sending miner fees in some transaction code I was writing. I mistyped the conversion factor converting from BTC to satoshis (raw bitcoin transactions record amounts as satoshis - 64-bit unsigned integers), published the transaction, and ended up sending something like 10 BTC instead of 0.1 BTC to the miners.
One possibility is that the transaction was injected by the same person who mined the block. Thus the same person who paid the fee collected the fee.