Roaring Rampage of Revenge: While he was locked up in Arkham between Seasons 1 and 2, a group of guards liked to beat the crap out of him on a regular basis (not that he didn't deserve it). In Season 2 he's spending his time hunting them down and murdering them one by one.
Tranquil Fury: Her demeanor after recovering from Scarecrow's fear gas.
"Well Done Daughter" Gal: One of the root causes for Harleen's eventual Sanity Slippage is her obsessive need to prove to her father that she is not like her mother, who ran out with another man.
You Look Familiar: Is played by the same actress who played Arkham's wife in season one.
Big Damn Heroes: "Matches Malone" is a geriatric man already written off as suffering from dementia before getting a knife to the back. Later, he staggers down the hall toward three Arkham inmates... whom he casually defeats in moments before The Reveal that Matches is Batman in disguise.
Chekhov's Gunman: Got a few offhand mentions and was the subject of an April Fools joke before appearing in person in Episode 17.
He Who Fights Monsters: In Season 2, to the point of recruiting Scarecrow to work for him by promising his old job and office back in return.
Trauma Conga Line: First, Arkham is carjacked by the Joker and forced to act as an accomplice to his kidnapping of Bolton. Then he is taken to his house, tied up along with his wife, and told that a bomb will kill her at midnight unless he follows his instructions. Then, after the church incident, he escapes in the middle of shootout between the Joker and Gotham police, only to be captured again after the Joker commandeers a squad car. Then, after being forced to sell the asylum to Lex Luthor, he watches as his house blows up with his wife still inside it. She survives, but is in a vegetative state with little chance of recovery. That in a nutshell is what amounts to his Start of Darkness.
Pragmatic Villainy: Ultimately considers acquiring Arkham Asylum more trouble than it's worth, and agrees to sign it back over to Dr. Arkham. However, Arkham thinks this is merely Lex Luthor Code for "As soon as I get out of here I'm paying a hitman to shoot you in the face", so he has Two-Face shoot Lex instead.
Punny Name: His full name is apparently Theodore Bayer. Say it out loud.
Of course he does work for the Joker. It could be an alias with the pun being intentional.
Wild Hair: In Season 2 he has long hair and an unkempt beard, making him look much more like a homeless bum than in Season 1.
Why Do You Keep Changing Jobs?: His claiming to have held wildly varying jobs is a Running Gag. It's unclear whether he's lying to try and make himself sound useful or whether he's actually a big enough screw-up to have had and been fired from all of those jobs. It's confirmed that he was at least telling the truth about being a GCN cameraman. He was married to Summer Gleeson while he was employed there.
Dr. Thomas Elliot
Bi the Way: Beds every guy he puts his eyes on, and Selina Kyle. He also leaves a message on Bruce Wayne's answering machine about Andrea Beaumont, who both he and Bruce apparently have a thing for.
The Casanova: Is apparently able to charm men into bed in extremely short order, usually starting with just a smile. Although, since they are men, this may have more to do with certainothertropes than it does with this one.
Mythology Gag: "I like to keep my involvement with the Wayne family Hush, Hush.