Other mistake: They show the tether and tether anchor fall out of the ship and fall behind, much in the same way as throwing something out of a car. However, it was still in the warp bubble and should have continued to be moving at warp 5 with the ships. We see later Columbia extend its warp bubble around Enterprise and Enterprise remains at warp 5 after cutting their engines. But, if the tether is no longer affected by the warp bubble, it should have been instantaneously out of view.
Suggested correction: Too much supposition, especially regarding fictional technology.
This correction is too vague and gives no counter argument to support the statement. Either it's affected by the Warp Bubble and stays at Warp 5 or it doesn't. Even with the inconsistency of warp speed, the ship is still traveling 20-30 million miles a second (23.2 million miles a second at standard speed). An object that small would be out of sight within a mile or less (fictional technology or not). Since we know the object isn't traveling at Warp 5 (otherwise it wouldn't fall behind as it did), it would have to be traveling at least Warp 4.99999999 to stay in range as long as it did (a speed never established in-universe). It's also been established in-universe when a ship comes out of warp, it has no inertia so it will not continue to drift. Given in-universe established facts about the fictional technology, there's nothing to support the idea the object is still traveling at Warp 4.99999999 (at Warp 4.9999999 the object would still be out of sight after less than a second).
