Octodad is all about finding the right rhythm of movement, so take your time when performing the tasks.
You will move better without the items, so instead of carrying them around, just throw them in the direction you want.
Most of the time there are a number of ways to avoid the enemies, so experiment with various approaches.
There is a secret level in the Aquatic Fun Center’s bathroom. If you sit on the toilet in the middle stall and flush it, the hidden level will begin.
Among the secret things in the game is the reference to another famous indie game - Stanley Parable. It is in the form of a poster that says 'Stanley’s Pair o’ Bowls.'
There is also, among others, a reference to the Surgeon Simulator, a game that also uses unorthodox movement mechanics. In Octodad, it is presented as a board game on one of the shelfs.