(Guess the reference!)

Time, matter, antimatter and space manipulation.  Almost anything he wishes to do to anyone he judges is  possible. 

 The Spectre is capable of warping and controlling reality. He can use his ability to control reality to simulate any form of superpower or ability from shapeshifting to warping time and space.

Levitation, telekinesis and flight.

Bioluminescence- Mainly focused through his eyes at times.   Or an entire sickly green mist around himself .

Power bestowal which could be explained by his connection to the Multiverse's energies.  He can bring out the fullest potential of someone else. Whether or not it's permanent has not been made clear .

Interdimensional travel and  Chronokinesis. Capable of separately projecting himself across multiple points to communicate with someone and guide them at whatever pints of time they're located in.  In other words astral projection

Invulnerability. - Even if it appears to go straight through him ordinary means and weapons do no harm

Limitless Strength

Energy blasts that stun, devastate or simply put people to sleep.

Spirit Physiology- The more typical abilities expected with the departed.  Some of which proven to be more dangerous than expected. Such as his Wail, powerful enough to shatter countless glass, barriers in Gotham and pushing away people for miles. (Pure Sonic Force.)

Creating shields that can cover, crush, and protect whatever they surround.

Fusing individuals with objects leaving them unreachable ot capable of being separated in any means.
Weaknesses 

Strong Magic can be sufficient enough to injury  , and even destroy  the Spectre, killing the human host as well. 

Reaching his limit, which lessens his power and makes him vulnerable. There are lines made, things he is not allowed to destroy, or alter which could result in the banishment of him.  Or at least the Spectre