Sometimes when riding in a minecart, the cart will suddenly stop on the tracks but the moving sound will still play, and all of a sudden you'll glitch forward to where you should be. I have not tested this in multiplayer, but I think that it appears normal to other people. You can still move your view around while this glitch is happening, and your framerate doesn't decrease. You get a bit of a lag spike when the glitch ends, but not too bad.

About the extreme server lag spikes: I was playing on the MineTrek server, and I had just warped somewhere, and all of a sudden my framerate dropped from over 125 to just 2, and it fluctuated between that and 0. Most of the time, though, it was 0. I had to disconnect, it lasted for over a minute, and didn't get resolved.