tolkiens legendarium - Did leaving out Tom Bombadil create any plot holes in The Fellowship of the Ring or any subsequent LOTR films?

The article Movie vs. Book: Fellowship of the Ring shows the differences between the book and film of the Fellowship of the Ring. This causes the film to leave out 4 entire chapters. Because of this, Tom Bombadil was completely left out of the film series.

Did this decision cause problems later by creating plot holes or situations that needed to be explained away which were not in the original text?

Answer

According to Tolkien himself, Bombadil is unnecessary to the narrative; as he notes in Letter 144:

Tom Bombadil is not an important person – to the narrative.

The only thing significant to the plot in the Bombadil episode is the finding of the Númenorean knives in the Barrow, which the movies also leave out. So we don't get to be aware of the fact that Merry's attack on the Witch-king was actually made with an enchanted dagger made specifically for that purpose; but that hardly seems to matter so far as movie-canon is concerned: if you ignore the fact that an enchanted dagger was needed to harm the WK, you can have Merry attack him with any old dagger just as well, and get the same result.

Letter 91 does note a foreshadowing in the Bombadil adventure that is of some significance later:

Frodo will join them and pass over the Sea (linking with the vision he had of a far green country in the house of Tom Bombadil).

In the movie, the description of the "far green country" is of course given to Gandalf (during the siege of Minas Tirith) and is entirely absent from the end of Frodo's voyage (which doesn't appear in the movie). Whether this is major enough to be considered a "plot hole" is probably too opinion-based for me to comment any further.