1) Installing tile directly to a plywood subfloor. This is technically an allowed standard, but the subfloor has to be at least 1.25” thick. Most people don't check the subfloor for the correct thickness

Although bonding tile directly to plywood is an approved method it does have a pretty specific standard that must be met. I have seen plenty of floors that did not meet this standard and because of this, the floor has too much deflection that caused the grout to start to break out from the joints. The best way to check your plywood subfloor for the correct thickness is to cut a sample piece from it. I recommend using a smaller hole saw for this because it allows you to get a core, and possibly replace it when you're done checking!

2) Not cleaning the floor properly before installing uncoupling membrane or tile

When installing an uncoupling membrane such as Ditra, the floor is supposed to be vacuumed and then wiped clean with a sponge and water. Unfortunately, I see many installations where it is only vacuumed. This allows tiny particles of dust to remain on the floor, which could act as a bond breaker. 

3) Starting the layout at the door with a full tile and ending up with sliver cuts in the field

When determining layout it is best to take time and figure out where it is best to start from. I see some installations where the installer chooses to just start with a full tile at the door and let it layout however it does. Although this can, and does, work occasionally it can also leave you with sliver cuts that don't look the best along walls, showers, and cabinets if you're not careful.

4) Not using the right notch size when installing floor tile. Having less than adequate coverage exponentially increases the possibility of cracking tile

Just like with any tile installation, using the proper notch is extremely important. If the wrong notch is used with floor tile it leaves the possibility of hollow spots, which are susceptible to breaking or cracking under small stress loads. I’ve seen this happen in an apartment I lived in. The tile was set with a notch that was too small and it wasn't back buttered, so when something fell on it from 3 feet up the tile shattered into tons of small shards. If the tile was installed properly this wouldn't have happened at all.

5) Not leaving expansion and contraction gaps against walls, curbs, cabinets, and tubs.

Expansion and contraction are things that get thrown around when working with wood products, but to most people, the thought of it relating to tile doesn't make sense. But, expansion is a huge deal with tile. If setting tile on a floor and the cuts are tight to the cabinet bases, the bathtub edge, and the wall framing, once the tile expands it could cause the tile to explode up from the floor. I know it sounds crazy. But there are videos of it happening online along with floors “tenting” where the tile becomes unbonded from the subfloor in a teepee look but doesn't explode upwards.