The invitation shown gives the time and date of the "Time Traveller" welcome reception as 12:00 UT (1.00 pm Cambridge local time) on June 28, 2009. A grandfather clock is shown clicking second-by-second to the appointed hour... but every shot of the full clock face shows it at either 5:00 or a few minutes before, with the date indicator (a 31-day dial) indicating the 16th of the month. Apparently the clock was shot at a different time and on a different day as the announced party (and possibly was at a different location.) And it does not appear in any shots of Hawking at the party. (There is a fraction-of-a-second shot of a very different clock face reading 12:00)
Or maybe the time travelers showed up at the right day and time...but the film crew and Hawking were five hours late...and twelve days early?
Near the end of the episode, when they are traveling on their hypothetical time travel ship, the narrator says they travel farther than possible. After two years they are traveling at 50% the speed of light. After another two years, they pass the nearest neighboring star, Alpha Centauri. Alpha Centauri lies about 4.25 light years distant. It would be impossible to pass it after only 4 years even if they started off at the speed of light.
After the time traveler in the white Tyvek suit steps through the portal, a display showing environment conditions is shown. On the second bit it reads "H20 CONTENT". Where the "O" should be in H2O, there is a zero. This can be identified by the line through the zero, an "O" does not have such line like in the word "CONTENT" on the same line.