Most complaints about espers are because of two reasons:
1) Telekinetic strike: need to stand still for 1,25s to cast, which makes esper the only class that has to stand still to deal a good bulk of their damage. THe issue is that there is no higher dps here, you'll do on par with other classes, so yes to penalty, no to bonus. This is the main reason everyone that played a spellslinger doesn't like the esper, but if you're familiar with casters and mobility issues, you'll do quite well anyway.
2) Spectral form is generally considered a weak skill for what it does. In reality it's quite good, except that it roots the caster, because it gives 5 psi, 1 interrupt armor and an absorb shield. Root has to go, hopefully it will.
Other valid complains are:
Blade Dance is useless and I mean 100% completely and utterly useless, in fact it'll kill you if you try to use it and something bad is happening while you're still channeling that PoS skill.
Concentrated Blade: theorically is awesome, being off the gcd it's free damage and free psi, but it has 2 charges and each charge takes 10s to regenerate, if they change that to have both charges recover in 10s, it'll be a very good skill to use on the move.
Bolster is a hot, with 2 charges, no gcd and gives a psi for each cast, so it's another psi builder you use to speed up your bird casting rate (mind burst, bird is the graphical effect and its nickname pretty much). The fact a hot is used to build up dps can be seen as a good thing or a bad thing:when soloing is good, in a raid it makes no sense.
Small hint: When you get to 5 psi, cast 1 more TkStrike and mash the Mind Burst button, due to the flight time of projectiles, you'll get your finisher and the supposed 6th psi will become your next 1st psi: this until changed, is a little perk that helps not wasting TkStrike casts and maximizes dps.
Psychic Frenzy is an alternative to TkStrike, a replacement if you choose so, you get it at level 11 and it's a psi builder that allows mobility, is melee range, but for now it does less dps, even if there is no real reason for this limitation, so expect it to be buffed up in terms of damage. In PvP is often used as the main builder for small team fights (duels, arenas). One raid boss forces espers to use this skill because that fight is 100% movement based. I like PF as a skill, I just wish it could do the same dps as TkStrike.
This class is certainly a WIP, but once you learn a few things, you'll love it, period.
The only thing that made me think, was healing using ui frames to target, but in large raids it maybe a very good thing in the end, especially to not miss the tank(s).
A few hours from launch, I finally took a decision and I'll play an Esper.