SSDD/WMG

Jack Hart is Gary Hart's son
This one is kind of obvious, he is Norman's godson after all. The Oracle probably brought him to the future so he could be a legendary CAS officer and command the Inglourious.

Tessa is Richard and Anne's daughter
She looks too much like both of them to be a distant descendant, maybe she was abducted by the Oracle so he could play with her.
 * Heck, maybe Anne really was pregnant during that one arc and Tessa was stolen as an fetus.
 * And now we know Tessa was found in a basket on a subway train with a note saying she was "very important" and whoever left her there didn't leave any trace of their existence.

Richard and Anne were on the Britannia
When Norman started his revolution Richard and Norman had a disagreement and Richard sold his properties to buy a lower-level cabin on the Britannia. Over the centuries his and Anne's descendants resorted to inbreeding a couple times due to a shortage of other foxes on their deck, as a result their great-great-great-great...(etc.)granddaughter inherited more of their genes than normal.

Trisha, the Maytec AI is Obfuscatingly Stupid
Supposedly she has more processing power than the Oracle but is dumber than "a box of hair" due to severe blocks on her intelligence. That just doesn't make sense, you'd think she could figure out ways around her blocks.
 * When Central tried to contact Maytec to find information about the Anarchist's new project Trisha kept him on hold for hours then connected him to Dwight, who she was ordered not to let talk to customers until a certain meteorological event in hell. By the time he actually got to speak to someone intelligent he was threatening to cancel all the CORE's deals out of spite and the Doctor was inclined to give him some non-disclosure agreement violating information.
 * "Sometimes the smartest thing you can do, is act dumb."

Tessa cheated
We all know that Tessa won Sticks from Julie Waterman in a card game, and that she wagered Tin-head, and that Tessa and Tin-head both have internal radios...