Plot hole: The first time they communicate with the "entity" in the spaceship, they find a correspondence between numbers sent by the entity and letters of the alphabet. The entity presents itself as "Jerry". Later on, the entity tells Dustin Hoffman, "Stop calling me Jerry" - and then Dustin Hoffman realizes that the number-letter correspondence was wrong, and the actual name of the entity was "Harry". But if that is true, how could they have communicated without problems before? The very first word that the entity used was "hello", which would have to be displayed wrong, since it begins with an "h" and has an "e".
Plot hole: The government would have no chance of hiding the existence of the comet for a year. Most comets are discovered when they are very faint, literally thousands of times fainter than Wolf-Beiderman when Leo found it. Long before the events in the film take place, probably even before the government itself would be notified, the comet would have been discovered, an orbit calculated, and people panicked. The whole premise of the first half of the movie is thus based on flawed logic.
Plot hole: After Riker takes the Enterprise through the Briar Patch to communicate with Starfleet he returns to rescue Picard from the collector in mere minutes, even though it was supposed to be a 2-day journey.
Plot hole: Considering that this family has been training for the mission for years and certainly have received some instruction in astrobiology, they are awfully carefree around the cute little alien. Any real space farer would be aware of the enormous potential problems with first contact, like incompatible biochemistry (aliens might exude deadly toxins from their skin, be eaten alive by human-exhaled oxygen, etc). They even feed it human food without analyzing the alien; again, this could kill it, make it chemically dependent, cause it to go into a mating cycle, etc. But it's cute alien, so naturally they don't worry about any of this.
Plot hole: If Marybeth was able to seal her nostrils and use her extended finger to remove the cap and make nobody suspicious about her, why didn't Delilah do the same thing? She was alien, so she should've still been able to do it, same as Marybeth.
Plot hole: The rape scene in the parking lot... there is no one around for THAT long? But wait, once the detectives come in the scene two people are walking in the background with a shopping cart - they must have seen something!
Plot hole: Batman finds at Belson's home a handwritten list of substances needed for a transplant. Why would Belson, a medical authority in the field that knows those things thoroughly, even write a list down? If it's for Freeze to procure him the material, why would it be at his house and not with him, and when did he even have time to be at home to do that, since he has been kidnapped by Freeze when he was driving on the outskirts of Gotham and taken to the oil rig? If he had time to go home, he at least would have changed clothes, he's still in the tuxedo he wore when he was kidnapped the night before.
Suggested correction: Only 3-4% of the visible universe has been discovered. Meaning this comet could have been discovered much later.