Due to the probabilistic nature of particles, is it possible for a photon to arrive at a location slightly earlier than the speed of light? Due to particles not having a specific location in space unless it is observed (i.e. it is a probability wave), would this mean that a photon can appear slightly ahead of where the speed of light shows that it should be (Such as 299,792,460 meters away from a source instead of 299,792,458 after one second). The principle of a photon not having a specific location, but rather a superposition of probable locations, as shown by the double slit experiment, it stands to reason that this applies to its location in the direction of relative motion. I feel like I am missing something that makes this line of thinking incorrect, thus why I am posting this question. Is this idea flawed, or is a photon's location (and thus the time at which it arrives a given location) in its direction of relative motion uncertain and thus probabilistic?
 A: This is tricky, because you have to ask yourself how you know whether it actually traveled faster than light or not.  The only way to be sure is to measure its position at both the beginning and the end.  And there are further complications.  When relativity is taken into account, you need to think about the reference frame of the measurement and other finicky details.  Another complication is that there usually isn't a great way of measuring a photon without destroying it, and you need to do two measurements.
Let's ignore the complications and assume that you can measure it at both the beginning and end of its path, and assume that we are using the standard model of particle physics.
In this case, the answer to your question is no.  When you measure it at the beginning, then for a brief moment, the photon's position is well-defined.  After that, the quantum field of the photon will "spread out" again, but it does so at the speed of light.  So there is no way to measure it at the end and observe it traveling faster than the speed of light.
There are a variety of other complicated concepts that could play a role in slightly altered scenarios, such as virtual particles, but they are not relevant here.
Occasionally over the years, someone makes a measurement that seems to indicate faster-than-light travel.  One such incident occurred a couple of years ago when a particle physics experiment asked for help saying, "We're observing something that looks like faster-than-light travel.  Can someone come and double-check what we're doing?"  In every case it has been found not to be true.  (In that particular case I think it had something to do with the electronics equipment they were using.)
