Not sure if I should actually be here, as I am one of the players, but I have some answers.
I have no interest in psionics and only allow them in Dark Sun games, so I have not familiarized myself with the Mystic class. However, Unearthed Arcana material is often purposefully overpowered or underpowered. This would be a concern I'd have, and would probably warn the player.
Warlock multiclassing always makes me think of Devil's Sight/darkness cheese, so I'd be wary of that or some other potential cheesy combo the player has found. That said, I'm scratching my head about what someone can possibly do with Pact of the Blade, Archfey, and Swashbucker, other than probably go first or take some fairly stealthy combinations. I don't remember exactly what UA Eldritch Invocations were printed, however.
Party looks fairly weak in overland exploration, but that somewhat will depend on the backgrounds selected.
Devotion Paladin and Necromancer Wizard can easily result in intra-party conflict if played conventionally.
Party is fairly magic heavy, meaning creatures with Magic Resistance and good saves (e.g., Demons and Devils) may be more challenging to them, while packs of humanoids are likely to be less so (most magic spells are written to work well against humanoids).
Hiya, Mr. Warlock here. Archfey is for a change of pace, as both of my previous Warlocks were Undying. Swashbuckler and Bladelock both key off of Dex and Cha, so I am not sacrificing points to be MAD. I will be a decent striker, since I only need to be within 5 feet of my target, and alone with said victim, to get sneak attack, then I can pull out without issue. My only invocation from UA is Green Lords Gift, so all the healing I get is maximized, to reduce some of my squishyness. Also, Feylock will give me a decent escape option, in a couple of levels IIRC, so I can mitigate even more damage. I will admit though, my AC is on the low end at 14. If it becomes a real issue, I will be swapping out my Fiendish Vigor Invocation for Armor of shadows. Also, by the glorious gift of the DM, I am packing the Elixir spell from the new UA, replacing a spell that didn't fit my character anyway, so I will be able to assist in either healing myself, or healing others. I will be dual wielding a Short sword and "Cutlass"(Scimitar as my Blade pact weapon), giving me decent number of attacks, and some handy riders. Lastly, if I find we are severely lacking in range and/or damage, I can grab another UA invocation as Feylock to summon a Bow as my pact weapon, and deal some nice damage with it (at the cost of spell slots.) That pretty much lays out my strategy for playing him.
Maybe it's the pessimist in me, but all I see is infighting: racial and professional. The elf doesn't like the dwarf, and the human sees the half-elves as half-breeds. Then the rogue of three levels is intimidated by the bard of six levels, the wizard makes the other magicians feel inferior, and the paladin wants to knock all their heads in for being less than perfect. But that's only if they're decent role-players.
On the other hand, if they're all from Sigil, you'll be just fine!
Human here, and no worries. I am a Pirate, so I have crewed with a whole melting pot of folks. No racism to be found, unless "Stupid" is considered a race. Paladin will hopefully be cool with my Pirate, as I am on a mission for Davy Jones to save as many people on land as possible, so that they can die at sea eventually. As far as the party will see, I will be Chaotic Good, doing anything possible to save as many people as I can. I might even throw myself away to save someone, if I think they will save more people than me. My souls' continued not-tortured-in-hell state relies on me pleasing Jones, so There is little I won't do to complete his mission.