It's not that ridiculous. They were using the ideological programming as their control, if they could take them out then so could their enemies, and if there was a way to turn them off then the enemy might figure that out and use that against them. Remember, this was a civilization that had been constantly LOSING those wars, so they needed something that could turn the tide and thus couldn't be defeated or subverted.
Aren't they explicit that that time period is actually the off-peak hours for the docking bay? And they'd certainly try to time it to take advantage of that.2) The docking bay for one of the biggest space stations in the galaxies that sees a large number of ships come and go every single day has one single guy checking customs and the dude just walks out after killing him. Seriously, that's just ludicrous.
Told to him by a friend and mentor that he greatly respected. It's made clear that Franklin couldn't conceive of his friend lying to him about it until he has proof that he did.3) The doctor simply accepts a very poorly delivered lie about the organic material being quarantined on the other end without even a cursory verification.
Selling them as artifacts would bring in quite a bit of money, but being able to show how they would could set him up for life with a job maintaining that. It was probably worth the risk for that. Plus, he was probably curious himself, and knows that if he sold them off he wouldn't get to work on them. Franklin's image of him as someone who was intellectually curious and fostered that in Franklin works to establish the dual motives.4) The guy that dug them up KNOWS they are weapons that attach themselves to people and control them, so wtf did he need the doctor for in the first place? That's more than enough to ensure a massive payday from the corporation he was working for, there is nothing logical he could hope to gain by bringing the doctor in and a massive amount of risk. He doesn't need to replicate them himself he just needs to sell them to the corporation for more money then he could hope to spend.
My understanding is that that is a secure lab, which means that it can and probably is sealed off from the rest of station. Besides, they already passed quarantine on the other end, remember? And if I recall correctly the helper was in fact packing them away for the night when he gets infected.5) Their examination of the artifacts is utterly ridiculous. They are examining ORGANIC artefacts. They have no quarantine procedure in place, they handle them with their bare hands, and they lay them haphazardly around the lab allowing them to contact any number of different substances and surfaces. Then they just leave them lying out in the open on the table when they leave - despite knowing that this kind of tech is utterly unprecedented and extraordinarily valuable.
Didn't they establish that that was because the shot happened before it could fully recharge?6) The weapon fired by the soldier is explicitly said to go up in power 20% every shot, one of his first shots has enough power to totally disintegrate people, a later shot has the power to burn through hardened doors and bulkhead, and yet after that Sinclair gets hit directly by the same weapon and is not only NOT vaporized, he only suffers a minor wound.
Garibaldi calls him out explicitly on this at the end of the episode, positing that Sinclair keeps taking all of these chances because finding something worth living for after the war is harder than finding something worth dying for. Sinclair admits that he doesn't have a good answer for Garibaldi.7) Wtf was Sinclair doing there in the first place. Him taking a fighter out I could understand as he's a pilot and he was explicitly looking for an excuse to get off the station, but him being with a security team confronting a humanoid combat threat on the station is utterly ridiculous. That's what he has a security chief and personnel for.
It's also done reasonably well, as it appeals to the underlying logic that it destroyed its own planet, the one thing that it was ideologically bound to care about. My only quibble is that the machine would have been more likely to self-destruct than separate.The final kill-it-by-talking-logic is stupid but its a trope that appeared quite often in many shows (several times on Star Trek), so I can't really call that a plot hole.