As noted below, Season 1's In Spite of a Nail ending can explain virtually any "inconsistency" in the second season (ie: Abby suddenly knows martial arts and loses interest in Stephen; Connor becomes more reserved but has actually fallen in love with Abby; Stephen's alleged girlfriend Allison is never mentioned again, and neither is Connor's friend Duncan). These changes are even more plausible when you realize that Leek has been keeping creatures from various time periods and they're never sent back, which means the present is still being altered.
In Season 4, Duncan features once as the civilian of the week.
At first glance, the greater preponderance of dangerous animals that arrive via the Anomalies seems like a case of More Predators Than Prey. But when you stop and think about it, predatory animals tend to be more mobile, curious, and brave than herbivorous ones, which would be reluctant to go anywhere near something as weird as an Anomaly in their own time. It's the carnivores that come through, because they're the only ones with the nerve to approach a big sparkly glowing thing in the first place. The few non-predatory species that do wander into an Anomaly are either very large animals that wouldn't be as timid as the average leaf-eater, or (in the case of the dodos) too naive about danger to avoid strange things.
Emily's original fate. In 5x02, Abby gives Matt a newspaper article that tells him what happened to Emily once she went back to her own time: her husband had her institutionalized for the rest of her life. The condition of 1800s psychiatric hospitals are questionable at best. She probably did not live a happy or healthy life in her own time, but fortunately she comes back to the present when Matt goes to 1868 in 5x03, erasing that timeline.
The last series ends with a warning that something bad is going to happen to the ARC team. When Andrew Lee Potts shows up as Connor in the Primeval: New World season finale, he's with an entirely new team. Just what happened to his former teammates?