Is my furnace limit switch tripping due to a flawed coil installation?
That looks like a crappy install the coils should be sealed tight to the air handler. It can be repaired with flashing and screws or pop rivets. 
The reason your coils are running hot is the air is not forced through them this will have a huge affect on the efficiency and probably shorten the system life. I would get it sealed soon it can be done DIY just be carefull when drilling or screwing the flashing in place. I will usually use a bead of calking to seal the metal because air passing through a screwed flat piece of flashing without sealant can squeal quite loud, just a bead prior to screwing together makes a tight seal.