The main thing is giving up a lot of your privacy. The remote node could theoretically log all the transactions you receive and send, and also log your IP address (unless you use Tor, but then you are connecting through an exit node which raises other issues).
In terms of security from the perspective of losing coins there is little to no risk, as your private keys remain entirely on your own computer. The main thing is that the remote node could, in theory, serve up fake blockchain information to you and trick you into thinking you received a payment when you really didn't. If you then delivered on your end of a trade on the basis of that false payment information, you could lose money. That's pretty far fetched though, and in practice there is little risk of losing funds.