How so? If the electrum servers are nodes, then the wallet only needs to trust the servers, because the servers are already verifying if the blockchain is good or not.

However trusting the electrum servers is easy, just restart the client a couple of times and you get a new RANDOM server each time. If the TX data is the same every time, then it proves that the blockchain you are on is genuine.

We'd need a way to verify that these full nodes are really full nodes to be rewarded. We should find some way of having a full node perform some work to prove they're not just a fake node. Maybe they could perform some sort of mathematical computations to prove they're real. And then when they find the right solution to this mathematical problem, we reward them with, say, 25 bitcoins. I think this would work. People would love such a reward and so they will run lots of full nodes!

Number of nodes is not a problem. At least for security of the system. What could they do? Transmit invalid transaction / do not transmit a valid transaction.
Honest nodes and miners will ban those nodes straight away. They only good to spread the FUD across the system. And they already tried it with BitcoinXT. However, it is a psychological  (social-engineering) attack not a technical one. What they tried to do, is give an impression that a lot of people moved to their client. And probably, most of those nodes were running on single server.

Could similar attack happen in the future? Yes, possible. Maybe, it's already underway  with Bitcoin Classic. But those attacks not stand a chance against bitcoin protocol.