In The Two Doctors, The Doctor and Jamie are sent to Space Station J7. In light of The Doctor's comment that "officially, I'm here quite unofficially", it's likely that this mission was performed for the Gallifreyan CIA rather than for the High Council. The Doctor seems unable (or unwilling) to explain Victoria's sudden desire to study graphology to Jamie.
The Doctor's encounter with Shakespeare must take place after The Chase, in which The Doctor and companions see the Bard at Queen Elizabeth's court while using the Time-Space Visualizer. Had the meeting occurred before then, it seems certain that The Doctor would have mentioned it.
The Doctor's various adventures in China can only happen after Marco Polo, since The Doctor says in Power of the Daleks that this was his only previous visit to the country.
There's no onscreen evidence to support a meeting with the Daleks on Mars, but The Third Doctor isn't surprised by their appearance in Day of the Daleks, suggesting that he knows they survived their "final end" in The Evil of the Daleks, and since most of the Dalek defeats The Fourth Doctor mentions in Genesis of the Daleks are those of which he has first-hand knowledge, it seems plausible, at least, that this is no exception.
The encounter with the Drogue of Gabrielides mentioned in The Sun Makers seems out of character for The First Doctor, who rarely interfered on such a grand scale.
The Master's desire to destroy The Doctor must date from The Second Doctor's era, since The First Doctor doesn't recognise his classmate in The Five Doctors, but by the time of Terror of the Autons they've become adversaries (and a line in The Five Doctors seems to suggest that The Second Doctor is aware of his old friend's villainy).
The adventures in which The Doctor encounters Cleopatra's guard, and in which he is wounded at El Alamein, take place in Africa, which The Doctor doesn't visit for the first time until after Planet of Giants. I place them in Troughton's time as they seem out of character for The First Doctor.
The Doctor's assistance with a cure for the space plague fits the idea that The Doctor was performing missions for the Celestial Intervention Agency, since without this cure it's unlikely that the Draconians would be strong enough to assist in the Dalek wars mentioned in several stories.
The Doctor and Jamie's encounter with the Cybermen on Planet 14 is an unseen adventure, since none of their televised meetings with the Cybermen take place before The Invasion, at least in the Cybermen's timeline.
The meeting with Lady Peinforte is suggested by her statement in Silver Nemesis that The Doctor is "still little", a description which could only apply to The Second Doctor. Since that incarnation is almost as manipulative as The Seventh Doctor, the other events mentioned in Silver Nemesis would seem likely as well.