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Less than twenty pages into Trading Futures, and the Doctor has already blown up the Big Bad's stealth hydrofoil using nothing but a parachute, a cricket ball, and a cup of water. MacGyver would be proud.
From Book of the Still, Fitz's VR fantasy: The evil Doctori getting married to the virgin bride who turns out to be Fitz in disguise. Fitz and Doctori have a swordfight, whilst Fitz is in his wedding dress, and then Fitz escapes with a jetpack. Yes, really.
How about the scene in Alien Bodies, where the Doctor is being interrogated by UNISYC (a sort-of evil alternative UNIT) in a skyscraper? He escapes by bodily hurling himself through an umpteenth-storey plate glass window. A stunned Mook observes, "Nobody could have survived that fall." The UNISYC head guy's flat response? "If anyone could...the Doctor could. Find his body." (Needless to say, he does survive, through pulling off a trick later ripped off shamelessly by River Song.)
From the same book, a lone Kroton (much-mocked one-off monsters from the Troughton years) convincingly taking out AN ENTIRE BATTLESHIP'S-WORTH OF FREAKIN' DALEKS.
How about the lengths the Doctor goes to rescue his daughter in Father Time? He hijacks a NASA Rocket so he can reach the ship she's trapped on. When the villain contacts him on video-link and mocks how the ship's computer is controlled only by his voice, the Doctor promptly imitates the villain's voice and tells the computer to switch itself off, shutting down the ships defenses and allowing him to board. He makes it all look easy, with bonus points for having amnesia at the time!