There are two ships docked with Skylab, yet several outside shots of the Station clearly show only one ship docked.
Steve is not wearing any radio equipment when he is moving around inside Skylab to get to the other docking door. yet he is heard communicating with Houston Mission Control.
During the reentry, Steve gives their altitude as 700 nautical miles. Skylab never orbited above 300 miles.
During the training sequence, Steve warns Kelly of the danger of "gimbal lock", during the reentry sequence the "8-Ball" shows as being in the position of gimbal lock.
It would be impossible to send up another rocket at such short notice; launches take months of planning just to avoid collisions with orbiting objects, debris etc.
When Steve is assisting during surgery he is supposed to keep all surgical instruments clean and sterile, however he rubs his eye with his surgical gloves on and then touches the instruments that the surgeon is using.
Although the explosion happened in the command module, the Athena One service module appears to have the exact same damage as Apollo 13's service module. This appears to be re-used footage from that actual space flight.
Even if Steve's bionic eye is not working properly he could always close it and use his normal eye to see.