Why does Duckworth act menacingly towards the triplets, particularly Huey? Because over the course of the episode, Huey regularly dissed Duckworth when somebody compared their party planning skills, so Duckworth justly felt insulted.
Also the triplets, Louie mainly, were responsible for allowing Scrooge’s enemies inside the manor putting Scrooge at risk, something it was noted would never had happened had Duckworth still been around so Duckworth would’ve been upset at the triplets for that also.
Beakley admonishes Webby for bringing a crossbow, but approves of a regular bow. Why? Because regular bows tend to take more training and skill to use well compared to crossbows, and of course she wants Webby to hone her skills.
Crossbows are also Awesome, but Impractical, if you can use a normal bow. They have to be carefully calibrated, the strings have to be much thicker, and they take a lot of effort to pull back. A bow, if you're sufficiently trained? Well, see any trick shooter.
Webby's bow isn't just a regular, however, but a compound bow, which suits perfectly for someone with smaller stature; a compound bow uses a pulley system to produce more power for a person without the musculature or height that a serious combat bow would otherwise require.
While the episode did not feature notable nemesis Magica DeSpell amongst the other party goers (for obvious reasons), it did feature a magician of the black arts and first showcased Scrooge's dislike of magic in general. So in a sense ALL of Scrooge's enemies were in his mansion the night of his birthday.
The DJ Daft Duck helmet looks like it's supposed to assemble around the wearer's head to put it on, and then disassemble to take it off. That Dewey didn't know how to work the latter indicates he didn't Read the Freaking Manual before putting the helmet on.
