Lily says the Rental Car Company swapped out the car battery. Rental Car businesses don't do that. They would just give you a different rental car.
Unless Lily was studying Irish Sign Language before going to Ireland, she would not have been able to understand the Deaf Irish woman as easily as she did. Although Irish Sign Language and American Sign Language are sister languages, there are still major differences in the languages.
When three characters are sitting at a table, the American looks up at a wall with a small painting on it and says, "Look at the time". The actual clock is on the wall to her right.
The coffee cups that Lily is carrying at the beginning are obviously empty. Nobody takes a drink from any of them and at one point Michelle is holding hers sideways and nothing is leaking and spilling out.
Lily ran William off the road and then drove for miles in her car to the town but William who had to walk back to the town arrived not long after Lily.
Most of the action of the plot could have been completed with phone calls in one day, not by driving around for a week.
The deaf woman spends very little time watching others speak in group conversations. And her coworkers frequently commit deaf etiquette errors. For example,
1) The deaf woman is not looking at the boss as she talks about setting the leading lady up with the imaginary bachelor. The leading lady's "help me" would not have made much sense to the deaf woman, because she was not reading the boss's lips.
2) In the same scene, the boss walks back and forth and around in circles as she makes a speech. This effectively forces the deaf woman out of the conversation.