It seems that I saw Timecop ages ago, and I am almost surprised that it was in theaters as recently as 1994. Still, it predates my earliest published temporal analyses, and I may have viewed it before I began these efforts in 1997. What I remember is that it was an impossibly convoluted temporal disaster to which I was always reluctant to return to analyze. However, it's not always easy to find copies of the best and most current time travel movies, and people often ask about this one, so perhaps it is time to tackle it. It might not be as bad as first glance suggests--but it is, temporally speaking, pretty bad.
What makes the film difficult, though, is that the first temporal event we see (excluding the robbery of the Confederate gold, which has many of its own problems) is the last one the villain makes; thus we are in some sense seeing what is not quite the end of the story at not quite the beginning. It means that the history we see is not the original history, and that the history we see might be impossible. It will take quite a bit of unraveling to get to what happens; but there are a lot of other problems and complications in the mix as well.
These are also complicated by the "other" time machine, the one that someone else in the world apparently has, or perhaps does not yet have, or perhaps had first, for which we can only guess about at least some of what is done with it. However, ignoring that, and the Confederate gold trip which appears to have been connected to that, we can attempt to construct something of a starting point.
We begin in the mall. Melissa Walker is meeting her husband Max Walker, a police officer. We can note immediately that this is not a fixed time story, because later in the film the older Max is also here and alters some of the events (he stops the rollerskating pursesnatcher before the crime). We thus know that the thugs Max sees on the upper level are not there in this history. However, he is thinking of taking a new job with the Temporal Enforcement Commission (T.E.C.), which he has been offered by a colleague from the police, Commander Eugene "Gene" Matuzak.
That night his phone does not ring when Melissa is about to tell him she is pregnant; the only logical explanation for how Senator McComb and his thugs are able to ambush him is that they faked the call to get him out of the house (poor strategy, because it meant he was armed and wearing body armor, but they are not always bright). The Walkers are excited about the pregnancy, and he takes the job with the T.E.C.--he must, or he will never be targeted by the Senator, and his wife will not be killed. However, he never moves to the apartment in the city, because his home is not destroyed by a bomb and his wife is still alive and now with a family on the way they will want the space. And so the T.E.C. is formed, Walker is hired as one of its first agents, Senator Aaron McComb agrees to chair oversight of the program, and they begin trips to the past to prevent others from changing the past. The first of those trips ends our original history--but we know nothing about that trip, and indeed nothing about any of the many trips that follow it over the next decade. However, before we get to that, we have several other problems to address.