Karo corn syrup.
The way I heard it (direct from Nimoy, in fact) was that he was supposed to conk him on the head with the butt of a phaser. But that was 20 years ago, so I might be misremembering.
Right!
Also correct.
This would now be question 63.
These would be questions 64-67. Thanks!
Here are some question numbers for later ease of reference. Please read the OP. Thanks!
Pushkin, you’re right on:
- Commodore Wesley does call Kirk “Capt. Dunsel.”
- The phaser rifle does appear only in TOS “Where No Man Has Gone Before.”
As to 61, the unluckiest ship in Starfleet, the one I’m thinking of is even unluckier than the Defiant.
- They’re not orbiting it, but Sherman’s Planet is the one under discussion.
- It’s named after episode writer David Gerrold’s then-girlfriend.
Sorry. I lost track of what number we were on.
68 is up next.
Correct.
I was waiting for you to show up!
Ivylass, in Star Trek, prune juice IS prune juice! 
Good call on the gong and the matador, though.
Pushkin, you pretty much got the Tellarite question. Nice work in anticipating Trek’s propensity to do that, too.
Also, DrkGntly, Marc Alaimo didn’t play the guy who faked his death to get his hands on the metaphasic shields. You’ll have to go further back than that ;).
As for 57, that episode was on Spike today, so maybe a few more people know the answer now.
So, following up on the Kolvoord Starburst question:
68.) What formation were they supposed to be flying?
69.) When Captain Jellico took over for Picard in “Chain of Command,” what had his son just drawn for him?
70.) A point of rivalry between Riker and his dad involved sparring in a particular school of martial arts. What was it, and what did Riker learn about their competitions when his dad visited the Enterprise?
71.) Another Riker question: name the ships he served on before the Enterprise-D (bonus if you can name a significant event that happened on each one).
72.) In ENT: “Vox Sola,” what did crew members of the Enterprise do to inadvertently offend the visiting Kretassans?
Huh. I had no idea I had any kind of Trek notoriety. Awesome.
22nd Century New Jersey
He cheats but I can’t remember the name of the martial art. Some sort of nonsensical -jitsu.
The Potemkin, Hood, and Pegasus. He was inadvertently cloned in a transporter accident on the Potemkin, resulting in the birth of Thomas Riker, and was one of the few officers to side with Captain Pressman during a mutiny on it when they used an illegal phase cloaking device and partially embedded the ship in an asteroid. Nothing particularly noteworthy occured during his posting as executive officer on the Hood.
Oh, I beg to differ. At the time, you could say that it was the most important event in his career.
You were right on the other two, though.
Oh, I know! I know! He prevented his captain from beaming down into what he considered a dangerous situation. This brought him to the attention of Jean-Luc Picard, who was in the market for a Number One.
For all his firmness on the Hood, however, I never did see him prevent Picard from beaming down when Picard wanted to.
Can no one answer my questions? Are they too hard? 
- I believe the Hood was where he met Troi.
New question:
- All Betazoids have a specific physical characteristic that was intended to distinguish them for viewers, as pointy ears do for Vulcans and wrinkled noses for Bajorans. What is it?
Ivylass got it. He stood up against Captain DeSoto, and that impressed Picard. He met Deanna either during or just before joining the Potemkin. I think that’s only been firmly established outside of canon, though.
73.) All betazoids have totally black irises.
Doh! I should have thought before making a guess. Riker was on the Potemkin before the Hood, and knew Troi then, so they couldn’t have met on the Hood. Where did they meet? I can’t count this as a trivia question because I don’t know for sure. The Academy?
Ivylass, the miniseries was North and South, but I don’t know who else was in it.
Damnit, that’s what I get for posting in a hurry. I’ll rephrase: he met Deanna around the time he was posted on the Potemkin, but whether it was before or during has probably only been established in the novels. Remember, in the episode where they find his duplicate, Thomas Riker wanted to start things back up with her when he saw her again.
Also, what are you talking about, Ivylass? Unless I’ve missed some of your questions, all of your questions except the one about Jake and Nog and the one about miniseries Frakes was in have been answered.
Kaaaaaaaaaaaahn!!!
Way to go! I didn’t think anyone would get it so quickly.