Upon the time machine's arrival in the museum in 2017, John rubs his hand across the interior of the glass to clear the frost, allowing him to see out. The fact that he can see out shows that there is no frost on the outside of the glass; however in subsequent scenes the frost is on the outside of the time machine.
The number of H.G's house change. H.G tells Jane its 12 Mornington Lane, but later Vanessa says 10.
H.G. Wells states he has come from the year 1893. He then later tells Jane Walker that he is divorced, however H.G Wells did not get divorced from his first wife until 1894.
When the group in 1893 are discussing HG's marital status, one of them states "It is time for you to start dating". During that time period it would have been called "courting" rather than "dating".
Since Wells was highly intelligent, once the machine returned all he would have needed to do was go back in time about 20 minutes. Doing so would allow him to prevent the ripper from escaping. This would of course ruin the premise of the entire series.