When miners are working on their block, does everybody's block have the same transactions in them? On Bitcoin-Wiki's page about Blocks, it says that "Bitcoin transactions are broadcast to the network by the sender, and all peers trying to solve blocks collect the transaction records and add them to the block they're working to solve.". 

So, do all peers have the same transactions in their blocks at all times?
Miners will naturally be inclined to include those transactions in their blocks that give them high transaction fees (though exceptions exist), because apart from the block reward from coinbase transaction, those are the only incentives for miners. So, whatever transactions have reached a miner through the network, her choices will be restricted among those transactions. At a particular time instance, different miners most likely have different snapshots of transactions available to them. So, the answer is no (with very very high probability).