I would say that this can vary: there are some modes where they almost do no good for you and some modes where potato mines are very effective. In Turf Takeover, placing them in the objective or close to the payload are the best locations (this is especially good if you are on the defending team). In Surbination, place them in some of the objectives as you go from one to another, but spread them apart for best results. In Gnome Bomb, place them on the zombie tombs as it might vanquish any zombies that are trying to defuse them if not destroyed.
As of for other modes, they are not as effective but randomly placing them every so often as you go can net you free vanquishes, especially if there are no other zombie teammates to revive the fallen one, but at a minimum you will get XP for getting a vanquish this way, and can help your team push through as there will be less zombies to fight.
In any mode, I would suggest placing some of them as soon as you can if you are at maximum capacity of 4, as they take half a minute to recharge just 1. Remember to try and always spread potato mines more so that zombies destroying your mines are less likely to destroy all of them. Placing them where a battle is happening can really benefit you and your team if they happen to blow up some zombies.
Potato mines are one of the most damaging abilities, if not the most, that a plant has, so try to utilise them if and when you can.