Oh my god! I loved these screen savers to death when I was a kid! I used to watch the "Bridge Encounters" all the time and try to make an episode out of them.
The Enterprise intercepts a freighter. Exciting music plays. Picard thinks it's strange. I'd find it strange if a ship like that kept moving back and fourth for no reason, though I'm more curious as to why Beverly seems to be checking out Troi so intently. When they try looking at the ship again, the whole bridge crew becomes bored and they start playing the video game from "The Game". Finally, Picard says "Engage!" and they leave.
A station orbiting a planet/moon appears to be drilling into it with an energy beam. While the crew are observing, an Exocomp is trying to fix Riker's console station. Beverly is still checking out Troi. Worf starts to take notice, becomes jealous and Riker says "I think we can relax Mr. Worf." The space station still seems to be doing something to the planet/moon, but no one on the bridge does anything. Showing his true observational skills, Riker says "I'm not sure I have a specific recommendation." He probably doesn't want to say anything as long as the Exocomp is working on his station. Picard reacts to this by saying "Strange."
The dimensional rift from "Parallels" makes a return and starts spawning hundreds of Enterprise Ds. Riker, assuming that some of the Rikers onboard those ships are smarter than him, states "They shouldn't be so confident." Oh, Riker. They try hailing one of the Enterprises when one of them has Picard and Riker playing "When the Saints go marching in" on the bridge. Picard seems unfazed by this until another Enterprise hails them, prompting him to ask "What is going on here, Number One?". And he has a right to be concerned, because this Enterprise has Troi as Captain and Riker as Counselor. An awesome improvement. Q finally chimes in saying that these spacial anomalies is just another day at the office for him.
Picard gives the order to intercept... something. Turns out that it's a wild TIN MAN! Picard asks what it is and where it came from, seeming to have forgotten all about the incident back in Season 3. Riker, apparently his console still broken, has no specific recommendation. Beverly is still checking out Troi. Well now Picard has had enough, stands up, does his Picard Meneuver, and declares "I would rather outthink them than outfight them." while telling everyone to "Stay calm". When Riker asks what is going on, Q chimes in by stating that TIN MAN is part of a dangerous savage child race. Well, that convinces Picard enough that he orders the Enterprise to leave.
The crystalline entity returns! Picard orders an enlargement of the entity and to identify it. Unfortunately two wild squid entities from "Encounter at Farpoint" appear and threaten the universe with their display of public affection! But something is wrong. The glowing squids can't seem to reach each other. After continuing to try again and again, Riker comments "They shouldn't be so confident". Picard can't seem to understand why these two squids can't join tentacles with one another so he orders an investigation. Beverly comes onto the bridge again to continue checking Troi out. Riker, noting that his console still isn't working, gives up by saying "I don't know." Worf starts to get frustrated with these squids' attempt at showing their affection by saying that the Enterprise must intervene! Riker thinks they seem normal enough. Worf, thinking that the squids are now starships tries to hail them. He proudly tells Picard "No response, sir." Picard turns his head in confusion.
The Enterprise comes across a ship orbiting what appears to be the same planet that the space station was drilling into in Situation 2. Picard, now bored with dealing with Starships, decides to leave the system. Q chimes in on Picard's unprofessionalism by calling him a macro head. Picard bravely ignores Q's insults and says "Make it so."
The dimensional rift is still spawning Enterprises all over the place. One of the Enterprises attempt to hail them, and Picard orders "On screen!". It's the worn out, very damaged looking Riker. Apparently he has an eye twitching problem that won't stop. Picard shrugs this off by stating it is no longer amusing and leaves.
I hereby qualify this video as Season Eight.