There are any number of cases of friendly fire, both aircraft shot down by friendly aircraft or ack-ack and troops or ships bombed by friendly aircraft. RAF Fighter Command's first losses of the war were in the "Battle of Barking Creek" during which two Hurricanes were shot down by Spitfires; the Spitfire pilots (John Freeborn and Paddy Byrne) were court martialled but exonerated. In general, though, pinning down exactly what happened in confusing aerial melees was not at all straightforward, in many cases it's only careful post-war examination of accounts and wrecks that can resolve contradictory recollections and claims (and even then rarely definitively). There's a credible argument in Andy Saunders' Bader's Last Flight that the legless ace Douglas Bader was shot down by friendly fire in 1941 (and possibly two other Spitfires in the same "Circus"), but few encounters are studied in so much detail.

There are numerous anecdotal accounts in autobiographies; Desmond Scott's "Typhoon Pilot, for example, has at least three:

"While Umbers was firing at his 109, four of my boys arrived on the scene from Tangmere, mistook him for an FW 190, and scored several hits from behind with cannon fire"

"While Pat [Squadron Leader Pat Thornton-Brown] and his boys had been escorting three boxes of American Marauders, he was attacked from behind by a swarm of American Thunderbolts. Recognition signals had been sent out, but the inexperienced Americans continued their attack, and shot down Pat and a Canadian pilot, 'Chuck' Miller."

(After deploying to the continent the Wing flew beer over from Britain in Typhoon drop tanks, until:) "This arrangement came to a sudden halt when our aerial brewer's dray was attacked by American Thunderbolts twice in one day and was forced to jettison its beer tanks into the Channel. [...] The young Americans, who arrived late in the European war to fly the fat-bellied Thunderbolts, were full of enthusiasm but far too impulsive. Teaching them aircraft recognition was pointless as they would chase anything that flew - their own aircraft included."

In terms of anti-aircraft fire, that was always a danger; gunners tended to err on the side of incaution, hence the black and white "invasion stripes" painted on Allied aircraft for Operation Overlord. An early use of wing stripes was on Hawker Typhoons in 1942 as they were frequently mistaken for the Focke-Wulf 190. Frank Zeigler, intelligence officer of 609 Squadron, wrote in the RAF Flying Review about the results of the confusion: "Once a gunnery officer, whom I had just 'blitzed' on the phone, actually called back with the request: 'Could you ask your pilots tactfully - very tactfully - did we get anywhere near them?' Sometimes they did. Roy Payne, wading ashore after being hit and crash-landing in shallow water, really lost his temper when the coastguards addressed him in German." See also an Imperial War Museum photograph: "A Hawker Typhoon Mk 1B in fighter pen at North West corner of RAF Duxford (...) The black and white stripes painted on the underside of the wings - sometimes referred to as 'Dieppe stripes'- were actually introduced following the failed Dieppe Raid of 19 August 1942. Originally only black stripes were painted on but white stripes were added by December 1942 for greater recognition by other RAF aircraft who had mistaken the Typhoon for the German Focke Wulf 190."

One of the worst incidents was during the 1943 invasion of Sicily when 144 C-47 transports carrying paratroops flew over Allied ships that had been attacked by German bombers; the ships opened fire, shooting down 23 C-47s. As a result there was more training in recognition for naval gunners for Operation Overlord, augmented by members of the Observer Corps, and the distinctive "invasion stripes" were hastily painted on Allied aircraft from June 4th.