Just in the second episode alone I found so many problems:
* Why doesn't a race that uses holograms to disguise ships, have the technology to detect other ships using it?
Arrogance. They view species below their technological level as little more than animals. While they probably have technology that can detect holograms made by other races, the thought that their own technology could be used against them didn't occur to them. For the same reason that humans don't make monkey-proof guns.
* Are there no names on these aliens ships? No transponder signals identifying the vessels? It's amazing the Orville got in in that kind of disguise.
Again, arrogance. The alien race see themselves as almost alone in the universe, so therefore a simple scan that just distinguishes between their vessels and vessels of lesser species is enough for them.
And who knows, maybe their civilization has an anarchist mindset, and considers the thought of a central registry of ships, tracking each one, as abhorrent.
* Why is Alara in a position to command a ship? Sorry, but in the Trek universe which Seth seems to love so much, it takes years and years to get promoted just once passed ensign and simply putting on a uniform doesn't mean the Federation trusts you to be the third in command.
Picard: First in command, second ship, rank of Captain with decades of service.
Riker: Second in command, forth ship of service, rank of Commander with over a decade experience.
Data: third in command, second ship of service, rank of Lt. Commander with over twenty years in service.
The more experienced officer who would normally be in charge, was sidelined due to (lol) egg hatching duties. Alana was only supposed to have the com for a few hours anyways. And that is how you get experienced officers: By giving them responsibility, tiny pieces at a time.
* Goddamn the Union doesn't give a fuck. They aren't even trying a negotiation, despite that admiral's words -- just declaring them lost in the line of duty and replicable.
Well first of all, all experience has taught them that the Alien race doesn't acknowledge humans. Negotiations take two parties. Sending another ship on the remote off chance that they'll negotiate is incredibly risky. What if the aliens decide they need more humans for their zoo? Or perhaps a whole Union ship for target practice or to exhibit one?
Don't use your American puritanical standards on something that takes place 400 years from now. Drinking while on duty may be cause a moral panic in the US Navy today, but that was not the case in relatively recent times. In the British navy there was such a thing as a rum ration that was taken while on duty. The Russian Army also on occasion had vodka rations that were used before action or in cold conditions.
There's no reason to believe that the Union space fleet might also have a more relaxed/utilitarian view on alcohol 400 years from now.
* So, if the doctor has command after Alara, who is the doctor in a real emergency with wounded and/or casualties?
I suppose that the Doctor isn't the only member of medical staff, she probably has an assistant or second in command.