To start, they launched the Ranger from Earth on what appeared to be a Saturn rocket system, yet it is clearly shown later that the ship is capable of reaching escape velocity on its own. This is more continuity than science, but...
Next, we reach the wormhole. All seems great until they aproach the hole and it has a sort of skin showing the other side, while in fact you should see directly. When they pass through the edge, they have an odd period of uncontrolled flight as they pass through some sort of tunnel to the other side, even though they just correctly explained that a wormhole is a direct spherical aperture between two areas in space.
Next, they park at the L2 of the planet-blackhole system and make a trip to the plant because the time gradient is so strong that entering low orbit would be catestrophic. I question how such a planet is not volcanic with such forces at play and even be a candidate planet...
Next, we have the unexplained firey explosion from the airlock, then carnage followed by a redicuously rapid descent into the atmosphere which is then all-the-sudden a descent into the blackhole, which if it was actually a threat, the main ship would have been again parked at L2 and not been close to atmosphere at all (and if L2 is that close, again, gravitational forces, lava, and candidacy...)
Next, we have a lot of nonsense after passing the event horizon of a black hole
Finally, we have the hero embarking on what's sure to be a multi-year journey in what appears to be a fighter craft...

The first planet surface gravity was 30% higher, IIRC; however the passage of time was more like 1 hour to several decades. They were there like 45min and 23 years elapsed on the orbiting ship.

Maybe the Ranger is launched from Earth on the rocket to preserve fuel? I can't imagine the craft can hold much (hell, it may even have been refuelled on the mothership), in which case why waste a limited tank when the planet you're launching from has the means to launch you?

Yeah, beats me why they didn't just pass straight through. I expected them to go in one side and out the other almost immediately... but I guess that doesn't look as cool?

Planety physicy stuffs. Dunno. As for candidacy, seeing as time is warped, the beacon message Coop and Co. got may have not included data on the waves. It's obviously not a planet you can live on, but no-one thought to consider the relative age of the beacon message, jumping straight to the conclusion that the scientist who went down was competent and didn't set off her beacon in premature excitement the moment she found water.

The explosion when Mann depressurised the airlock? It looked to me like the explosion was caused by his Ranger smashing against the mothership, rather than as part of the depressurisation.

Where's the story in cold, hard physics ripping the man apart as he enters the black hole? For all we know, what the team classified as a black hole was a phenomenon subtley different to a black hole - after all, with the way "They" were bigged up, if a civilisation is advanced enough to do whatever the hell they did inside the 'black hole', they could fix it to not tear a man apart. Magic. Plus narrative.

I'm not convinced that Coop's final journey is going to take years. Cooper Station is in orbit around Saturn (so close to the wormhole, meaning the initial two year journey to get to that point isn't necessary), and Edmund's planet was never given an explicit distance from Gargantua. The 'fighter jet' Coop appropriated is tech 90-odd years more advanced, from a space-faring civilisation, than the ships from Coop's first adventure - you don't have to suspend disbelief by much to imagine that they may be a lot more capable than they look.

It was in a different star system. That's why they didn't visit it second

Oh, OK. I thought Edmund's planet was the farthest of the three orbiting Gargantua.

Remember at the beginning, they said there were planets in three different solar systems. I don't remember whether they explicitly stated that it was in one of the other systems, but if their fuel budget originally allowed for a round trip to one of these other systems (and it would have to, to maintain the ruse), then the dialogue about the fuel heavily implies it.

So I take back my other system assertion. The planets were all in the same system, and I see now that the first planet station keeping was quite further off than I originally supposed; without the advantage of L2, the station keeping would have been enormously expensive, as depicted.