In the hunt scene, you can clearly see that the riders are following on a path made by automobiles. The path has tire tracks all along.
In the scene where Tom Jones and Sophie Western are riding around on various horses within a barnyard area, one of the barn sheds in the background has an area of its roof repaired with corrugated iron. The story was set in the mid-1700s but corrugated iron wasn't invented until the 1820s.
One of the dogs on Squire Allworthy's estate is a Golden Retriever. It can be seen trying to follow Tom when he is banished from the estate. The film is set during the time of the Jacobite Rebellion which began in 1745. The Golden Retriever was first bred in Scotland in 1868, more than 100 years after the time when the film was set.
After Lady Bellaston reads Tom's letter proposing marriage, she wads it into a small ball, clearly wrinkling it. In the next scene, Lady Bellaston shows the letter to Sophie's aunt, but now it is smooth and uncrumpled.