I think it is necessary to have a good definition of the concept of time. I've not come across anything I consider good but then again I haven't tried looking since the internet has exploded with information. Here is an attempt at defining time: the observance and monitoring of a series of events (as compared to another series of events).
And here is one from dictionary.com - A nonspatial continuum in which events occur in apparently irreversible succession from the past through the present to the future.
If you consider my definition, you'll note several important points: 1) an observer is necessary, 2) the observer must monitor (or gage), 3) there has to be a series of events to be monitored (or gaged).
To consider time 'inconsistent' would mean that the gaging of a series of events varies. A variation in gaging could easily happen. This has probably even happened in a way that you can relate to. Think of an event that seemed to last longer than you would have liked it to, perhaps something like being in church when you didn't want to be in church. You keep looking at the clock (the gage) and the words being spoke, the actions being performed, and the beating of your heart (the events being gaged against) seem to indicate that much time has passed. But, the clock tells you that the service to now has only taken up a short period of time.
If the events being monitored happen to be spaced further apart the clock will tell you that the service has taken up a longer period of time. If you happen to be in church and there is someone there you wish to perhaps lock eyes with and tell in that briefest of all time intervals that you have an interest, the world is a great place to be, and would be even better if the two of you could get together and talk after the service, the clock is moving faster than the anticipated event(s). The clock is assumed to be regular as a gage but appears to be varying. Of course this is a psychologically induced varyance.
If you consider that the gage and the events can be influenced by various forces it is easy to understand how time can be inconsistent. If you are using as your gage the time that the sun is shining you may find that on certain days you can walk much further than other days. When you get a watch to give yourself a more regular gage you actually find out that the sun is shining for a different amount of hours at different times of the year and that is why you can walk x distance one day and x + y distance another day.
Consider that a metering system (clock) may be influenced in a different manner from other metering systems. Say you are using an electric clock to gage events and some outside force slows it down. Relative to the events going on around it time as gaged by the electric clock will have varied when compared to other events also being gaged and furthermore you have an atomic clock to prove that there was a difference along with a couple other types of clocks to back it up.
Now let's think about two atomic clocks. Send one out into space at a high rate of speed and capture it at a later date. Compare the times on the clocks and the one sent out in space reads an earlier time than the one that stayed on earth. Time has varied for the clock sent away. Its events (cycles) occured at a slower rate than the clock that stayed on earth. Whether it had to do with speed, changes in inertial frames of reference, or some other external force which was exerted on it the fact is time varied between the two meters.
To take the thoughts to another level, consider a situation in which all relevant clocks in a reference frame are effected by an external force and to the same degree. Would there be any way to tell that time is varying? No, because we've stated that all relevant clocks are effected to the same degree. All observed events would correlate for regularity with each other. The only way to tell that time is varying is by comparing events in one reference frame to similar events in another reference frame.
So, to support the statement that 'time is inconsistent' I would point to my definition of time and explain that consistency relies on the regularity of the series of events being used to gage it.