The issue that I have a problem with is the raven flying from Eastwatch to Dragonstone. Given the distance between the two the flight time would be at least a day or more, and all we see is a night go by while Jon and co wait on the rock. If more time passes, then I could see the raven making it in time and Dany being able to save them.
Other than that, the whole adventure beyond the wall makes sense. I may be in the minority of the Wight hunt making sense. Tyrion is right in that to convince people of the threat you either bring them to the AoD or bring the AoD to them. We know from Sam's conversation with the Maesters that they don't believe the threat is real, and likewise the majority of the realm doesn't either, including Cersei calling stuff beyond the wall grumpkins and snarks. It has been mentioned that Dany could've flown them up via dragon, but at that point she had no reason to believe them or risk her dragons health searching the cold north for hours or days. I do think that when Gendry sent word he would have indicated a general location for her to search.
The wight hunt accomplished several plot points for the war to come. It established the WW and Wight connection, we saw how effective dragon glass is for fighting them (everyone without flaming swords and valyrian steel had dragon glass weapons), the NK got his Wight dragon as was seen in season 7 promos, the war became personal for Dany with the death of one of her children, and we saw the relationship between Jon and Dany deepen and evolve.
I do think that the NK set a trap for the heroes in order to get his dragon. It's just too convenient that 1 Wight remained after Jon kills the WW. The wight then screams in order to alert and summon the NK and his reinforcements. Given the scenes of the NK interacting and marking Bran and shutting down his control of ravens when scoping out the army, I think that the NK possesses similar powers to Bran. If so, then he could've foreseen the expedition and rescue via dragon.