[Nate the Great]

RIKER: And what Riker might that be?
PICARD: Commander of the Enterprise formerly assigned to the USS Hood.
RIKER: That's right.
PICARD: Then you must be the William T. Riker with a history of insubordination. He was even once relieved of duty, during the Cardassian incident at Minos Korva.

This is a reference to "Chain of Command". I'm surprised that the name Riker isn't better known for that itsy bitsy thing called "saving the entire Alpha Quadrant from the Borg."

DATA: Perhaps these artefacts have a special value to the Romulans.
WORF: The Romulans?
DATA: These structures were built by the Debrune. That race is an ancient offshoot of the Romulans.

In the comic prequel to Trek 11 it was stated that Nero's staff was a Debrune artifact. Yet another example of the support staff trying to respect continuity even if the writers don't.

RIKER: A witness said they saw you vaporised.
PICARD: These mercenaries use weapons that can activate their transporter. It gives them the opportunity to beam things quickly, just by firing at them. That's what they did to me.

Are these projectile weapons, or some sort of energy beam that leaves a charge on the victim? Either way, there are further questions that must be answered.

PICARD: The site that I wanted to study had been raided. A lot of the artefacts had been stolen. The site had been practically destroyed. I wanted to find out who was responsible. I tracked them to that bar on Dessica Two. I must have asked too many questions. They captured me.

And you didn't inform Starfleet...because?

PICARD: What? Calder Two isn't just another archaeological site, you know. It's a Federation outpost there.
...
PICARD: They also have a minimum of two phaser banks and possibly photon torpedoes. Is that enough to worry about?

From Generations we know that planet-based torpedo/probe launchers exist, I just question their effectiveness in a battle situation on a planet. Firing on a target within the atmosphere would require thrusters which are slower than impulse engines, giving time for a counterattack. Firing on a target in orbit would create disturbances large enough to give the ship ample opportunity to return fire or move out of the way.

TALLERA: Do you enjoy living dangerously, Galen? Baran can kill you in an instant if he activates his control device.
PICARD: I doubt that he'll do that. I've increased the accuracy of the identification process by a factor of ten. I'm the best person to analyse these artefacts. Baran knows that.
TALLERA: He may need you now, but I know Baran, and I can tell you he's not going to back down forever. You accomplish nothing by provoking him.

A good point. I think that on some level Picard is enjoying playing out a Dixon Hill scenario in real life. He shouldn't be this dumb.

WORF: Commander, we are receiving some kind of signal from the mercenary ship. These are Commander Riker's access codes. He is attempting to shut down our shields.
TROI: That doesn't make any sense. He knows those codes would have been changed as soon as he was captured.
DATA: That is correct, Counsellor. He does know. Mister Worf, prepare to drop the shields.

We could have a jolly time debating whether or not Data has learned intuition since "Redemption," but I'd rather give the credit to his Holmes program.