There are lots of little tricks professional screenwriters have to overcome small problems in their scripts. Many of them have clever nicknames. One of those tricks is called Hang a Lantern on It.
The idea here is if you have something a little unbelievable, you can have the characters point to how unbelievable it is. If a character says, "Wow, did you see what just happened? That's crazy!" then the audience will understand that the unlikely thing has been done on purpose. If you ignore it, the audience could think it's just bad writing.
This works best with small things that are plausible but might seem like an accident. For example, in the scene in Raiders of the Lost Ark (story by George Lucas and Philip Kaufman, screenplay by Lawrence Kasdan) when Indy is talking to the FBI, the FBI guys seem surprisingly ignorant of Biblical history. So at one point Indy asks, "Didn't you guys ever go to Sunday school?"
Now of course it's completely possible someone wouldn't know much about the Ark of the Covenant, but it could also seem like the scene is more about explaining things to the audience (which of course it really is) and the dialogue could start to feel forced. So by having Indy make this little joke, it brings the forced dialogue into the world of the story and makes the agents' lack of knowledge part of the scene.
Sometimes the technique can be used to sell even big logic issues. In The Terminator (written by James Cameron and Gale Anne Hurd), after Reese has rescued Sarah Conner and is explaining to her what's going on, she asks, "So you're from the future, too?"
Reese's response: "One possible future, from your point of view. I don't know tech stuff."
And as simply as that they don't have to explain the time travel paradox. The characters acknowledge that it doesn't quite make sense, but Reese establishes that there is an explanation; it's just that none of them know it. The audience goes along with it - because they want to buy into the story - and the movie can continue on with the important stuff.
There are limits to this technique though. You can't use it to paper over real logic holes in your story. It's simply a way to address those small moments that might make the audience go, "Really?"
It's even better if, when you hang a lantern on a problem, you also provide an explanation. For example in Star Wars (written by George Lucas) it might be a little implausible that a farm boy could pilot a fighter ship. So, when Luke is given an X-wing for the final battle, a commander questions his abilities. And Luke's friend from back home reassures the commander that Luke was an exceptional pilot back in the day. Problem acknowledged and dealt with.
Here we start to bleed into another technique: Eliminating Alternative Possibilities. This is necessary when there is a simpler solution to a problem than the one you need the character to choose. You have to eliminate that solution as a possibility.
This commonly comes up in thrillers or mysteries where someone who is not a professional detective investigates a murder. When most people encounter a murder they don't investigate it, they call the cops. So why does your character choose to investigate themselves? You have to give them a reason. Maybe the cops don't believe them. Or the character thinks the cops have the wrong guy. Or the character is wanted by the police.
A smaller example is in Little Miss Sunshine (written by Michael Arndt). The story is about the family going on a road trip so the daughter can compete in a beauty pageant. But if everyone just piled in the car and took off for California, the audience might think, "Wait... why does the whole family have to go? Why would the teenage brother and the suicidal uncle want to go on this trip?"
So in the dinner scene the characters discuss who's going - hanging a lantern on the logic issue - then they go through all of the various possibilities and eliminate any alternatives. Grandpa is the little girl's coach. Mom can't drive a stick shift. They're not supposed to leave the uncle alone. And so on.
When you give trusted friends your script to read, one thing you should ask them to do is mark any place where they thought something was unlikely (sometimes people not involved in filmmaking are better at this, by the way). If it's really a logic hole, you may have to fix it. But if it's minor, you might be able to solve the problem by hanging a lantern on it.