What are the random/luck factors in Puerto Rico?
The first random thing that happens in Puerto Rico is turn order.  This can be offset by having players bid on seats.

If you are playing with the expansion, then the buildings available are randomized. This can also help to prevent the game from being solvable.

There are the plantation tiles as described in the question.

Finally, if you are playing with more than 1 other person, player actions are, in a way, a randomization.  Some moves become better if your opponents act perfectly logically, others are better if your opponents make mistakes, and you can't know what they will do.  This is unlike chess (or a 2 player Puerto Rico game) where your opponent making a mistake cannot be a detriment to your game.

Overall, Puerto Rico is a very low luck game with all randomization being "input randomization".  This means that all random factors are chosen early in player decision, and by the time a player acts, they will know the result of at least that action.