Not enough damage output to be primary damage.
Not enough resistance to tank.
Its one Heal isn't strong enough, nor does it recharge fast enough to properly provide support.
No mez protection.
Essentially, a lot of the same complaints that one keeps seeing about Sentinels, with a lack of mez protection on top of it.
The Peacebringer's only saving grace is its versatility, with a plethora of powers available to the archetype that can make any two PBs vastly different from each other.
I remember the old days, when having a PB on the team was considered more a burden than anything, even though through their inherent power, a Peacebringer was intended to be whatever the team needed. More Blasters and Scrappers made it tougher, more Tanks and Defenders made it stronger, Controllers gave it that mez protection (-ish, it's actually resistance, which makes mezzes shorter) that was oh-so-sorely lacking. However, they came with that nasty possibility of spawning a team-killing Shadow Cyst Crystal, which would spew a full team of Nictus clouds for each member on the team, blasting everybody to pieces unless somebody buffed the Hell up and ran a Bolivian Army Ending against the crystal in the vain hope that the resulting explosion would destroy the entire spawn. This has, of course, led to a stigma that continues to this day, with people forming teams loathe to invite Peacebringers and their Warshade cousins (while the opposite is true for VEATs, which were apparently designed for stronger raw synergy with teams, so players often enjoy inviting VEATs to their teams).
So, that said...
Improvements that can be made:
Peacebringers would definitely benefit from a stronger front-loading of damage output. I imagine Corrupter-range damage output rather than Defender-range. It shouldn't take a full team of Defenders and Tankers just to bring a PB up to par.
Protection from Holds, Sleeps and Stuns should be worked into the resistance auras. This is an archetype that's supposed to be a variable threat response, but it keeps getting clonked over the head and kept out of the fight by everything past level 10. This means the PB better have a strong alpha strike, or they're gonna faceplant and serve little better than as vengeance fodder.
Glowing Touch seems superfluous. It's nice to have, but it largely goes unused. The time when we get it, we would also much rather invest enhancement slots into our attack and resistance powers. Speaking of superfluous, Quantum Flight could probably get the axe, too. With Quantum Acceleration, we get the intense speed boost the same as we see in Afterburner. I'm sure some folks like the Stealth it provides, but this stealth is unreliable as it keeps phasing in and out every thirty seconds. Last thing you'd want is to suddenly phase in as you're passing by a Rikti spawn on your way to fight Dra'Gon. Tweaking these powers or finding powers to replace them would be nice. Maybe a debuff for the enemy to replace Glowing Touch or add some other buffs to it. Maybe a team buff in a similar vein to the VEATs.
My take on the alternate forms is less intense because I don't use them. The times I have, I've found them lackluster. The Bright Nova has no defenses and gets cut to pieces easily as its powers don't recharge quickly enough to defeat even the most basic spawns. The White Dwarf has nowhere near the same resistance as a tanker, nor does it have enough attack powers to properly wage combat with the enemies. Both forms suffer from a lack of access to human-form powers, and investing in the alternate form powers restricts one from investing in their human form powers. The AT gets way more powers than it gets enhancement slots to properly outfit when you go for alternate form builds, with the speccing for Tri-form needing the player to be very precise, both in build and tactics.
One improvement I can suggest on this front is granting access to human powers in alternate forms. This would go a long way toward improving their versatility, with the Nova gaining more resiliency and the Dwarf getting more damage output.
And... That's all I've got for now.