Making the Game Harder
Game Bugs
Excessive Firepower
Blaster Launchers
To put it simply: the weapons are too powerful and thus the temptation to overuse them too great. Completely destroying a map is fun at start but butchering the aliens gets boring after a while. Either do not use the weapons or only bring 1 on each mission.
Enlarged Squads
Restrict your squad regarding soldiers and tanks. Never bring more than 20 units into a battlefield.
Don't use Psionics
[Psi-Amps] completely unbalance the game towards the human player. Even 1 Psi-Amp is bad enough for the aliens, but to bring a squad full of psi-trained soldiers will mean that all the aliens will be mind controlled during the first turn (including even [Cyberdisk|Cyberdisks] or [Sectopods|Sectopod]. Once you start, the uncertainty and the risk will go down, and so will the fun.
The same applies to [Mind Probes|Mind Probe] since those devices can be used to screen aliens for their rank or to check if they will reaction fire.
Finally, the use of [Psi-Labs] should be restricted to screening troops but not training them, since they can't use Mind Probes or Psi-Amps. A harder setting would be not to use them at all and only find out during a fight who are the psi weaklings.