Whenever I'm watching footage of battle in the pacific, I often see planes being followed into the sea with anti-aircraft fire...to the point that when they hit the water, you can see the lines of shells hitting the water behind them as gunners keep tracking them all the way down.
Given the number of men that covered them, I have to imagine that this would be a real problem to other ships in the group (granted, much less than a kamikaze or bomb/torpedo) as they'd be hit by their sister ships while following said planes.
I assume that most of the "ak-ak" fire would be limited to the outer ships in the group, in order to prevent this, but you still see video of ships being "in the firing line" of the other ships while fighting off incoming planes.
Are there any/many reports of friendly casualties (ship or human) due to this misdirected fire?
It was not unknown for anti-aircraft fire to hit other ships in the same task force. The Royal Navy recorded four incidents where damage was caused to ships by anti-aircraft weaponry, though one of these incidents was the ship causing damage to itself, and another was a ship being mistakenly targeted with anti-aircraft weaponry used in an anti-surface role.
The first incident came on the 19th November 1941, while the destroyer HMS Garth was escorting a convoy southwards down Britain's east coast. Garth was detached from the convoy to search for suspected E-boats (German torpedo boats, which frequently attacked convoys). Meanwhile, the destroyer Campbell was also independently searching for E-boats, travelling northwards. The two ships ran into each other at relatively close range. Campbell misidentified Garth as an E-boat, and opened fire with her anti-aircraft weaponry, with Garth returning fire with her own equivalents. Garth took six hits from Campbell's 40mm pom-poms, which caused serious damage. One hit caused a fire in her forward magazine, though this was quickly extinguished as the shell hole was underwater. A second flooded her forward boiler room, and contaminated the feed-water for the aft boiler room, immobilising the ship. A third burst inside the engine room, breaking a steam-pipe to one of the engines, further immobilising the ship. Two men were killed and eight were injured. Garth survived, being towed back to Harwich for repairs, while Campbell would go on to sink three E-boats in a later engagement on the same day.
The next came on the 8th November 1942, in the Mediterranean. The cruiser HMS Sheffield was operating in support of the Operation Torch landings on the coast of Algeria and Morocco, when she was attacked by torpedo bombers. She engaged it with anti-aircraft weaponry, including her main battery of 6in guns. Shortly after it was fired, a shell, likely fired by the central gun of her forward ('A') turret, burst. This scattered splinters all over the ship's bow, with much of the ship suffering minor damage. Sheffield was able to continue operations unaffected by the damage.
On the 9th June 1944, the ships off the Normandy Beachhead came under attack by German aircraft. The attack was met with a hail of fire, quite a lot of which didn't hit the target aircraft. The minesweeper Tadoussac was struck by one of these shells, a 3-4in shell fired by a ship nearby. This shell passed through the ship's minesweeping deck, cut a steam pipe and damaged the lubrication system for the ship's stern tube, before coming to rest in someone's cabin without exploding. The damage was straightforward to repair, but was hampered for a short time by the fact that several corridors were full of steam from the damaged pipe.
The final recorded incident came in the Pacific, on the 29th January 1945. The British Pacific Fleet came under attack by Japanese aircraft. During the attack, the carrier HMS Illustrious received two hits from 5.25in guns, fired by one of the escorting cruiser Euryalus. One shell hit Illustrious near the radio room, causing intensive splinter damage, and destroying a radio transmitter. The other hit the bridge, destroying one of Illustrious's twin 20mm Oerlikon guns, and damaging the radar aerial and rangefinding equipment. This shell also caused splinter damage to two aircraft on the flight deck, setting one on fire. Both aircraft were thrown over the side. Twelve men were killed and 21 wounded.
There were many more incidents of this type that occurred during the war, though not necessarily to the RN (and hence were not recorded). During the Battle of Okinawa, the USN would suffer 12 ships damaged by anti-aircraft fire from other ships. During the Battle of the Atlantic, it was quite common for AA gunners aboard merchant ships to ignore the safe arcs, and trail bursts across other ships in the same convoy. Other incidents did not cause much damage to the ship that was hit, and were thus not recorded by the RN. One incident in this category came from the British Pacific Fleet. After an anti-aircraft practice while the Battle of Okinawa was going on, the carrier Indomitable made the following signal to the nearby battleship Howe:
One of my Aircraft Handling Party was struck painlessly on the buttocks by a fragment of shell fired during Serial 5.
Howe's response was rather more comedic than might be expected during wartime:
Your 0950. Please convey my regards to the rating and ask him to turn the other cheek.