I downloaded a number of apps that could help in a ghost hunt, then I realized that my group doesn't take phones into the investigation area. They tend to make noises, even when 'silenced', and can give off random emf spikes when doing things like switching towers or even just signal areas.
But, if you're interested, here is what I found:
Bubble Level - It is useful for testing the floors, cabinets, shelves, etc., for levelness. Unlevel floors and stairs can cause slight vertigo, especially if they don't all slope the same direction. Unlevel shelves and cabinets can explain items 'flying' off them. And these can all explain items moving in odd patterns 'unassisted'.
SpectralView - Real time audio spectral analysis. Granted, it doesn't record, but it will show you, in real time, if the sound you're hearing is actually being generated by something physical.
Voice Recorder - Does exactly what it sounds like.
Tricorder - It has a built-in mf detector. Unfortunately, it gives off enough noise that it would contaminate any audio you have running, and it is not emf. You can take a magnet underneath it, rotate it, and get fluctuations. Really, it is just a cheap K2, which is pretty worthless in my opinion.
Metal Detector - While it doesn't fit into the 'standard' kit, it can be useful for finding things like speakers in walls, motors, and such if you suspect you're being played.
What I would really like to see is a combination of SpectralView and Voice Recorder. All of these are free, but I know at least 1 has a paid version.