My only complaint about the previous incarnations of Splinter on film is that he simply looked too frail to have ever taught the turtles martial arts. He literally didn't move at all. He was a muppet. Like a stick figure with a rat head.
There are strengths and weaknesses of the '87 toon origin and the Mirage origin. Mirage is stronger regarding the ooze, while the cartoon's explanation is super weak. For instance, in Mirage the ooze basically mutates the creatures to humanoid proportions regardless of what they were last in contact with. Meanwhile, the cartoon says it mutates the turtles and Splinter according to what they were last in contact with. The problem with that being, of course, that they depicted Hamato Yoshi cleaning the mutagen off the turtles and never coming into contact with a rat. The logic used in their mutations is that the turtles took on humanoid characteristics because they touched Yoshi... but Yoshi took on rat properties because he last came into contact with a rat and yet he clearly last touched the turtles themselves. So why wasn't he also a humanoid turtle?
That said, the merger of Hamato Yoshi and Splinter totally makes sense of how Splinter knows, and is able to teach, ninjustu. The Mirage origin(which is also the movie origin) makes no sense on this part. A pet rat stood on hind legs and mimicked Yoshi's martial arts training? Really?