Other Problems In Time Travel

The "observer effect" (see previous post) means that the Time Patrol causes a lot of its own problems so you may well ask: why are they there? However, in six of the thirteen works (counting the tripartite novel as three), they address problems caused by others:

individual time criminals;
Neldorians;
Exaltationists;
a personal causal nexus.

Like James Blish, who was a comparable hard sf, fantasy and historical fiction author but with a much smaller output, Poul Anderson was a restrained writer. The demons won Armageddon at the end of Blish's Black Easter but were not allowed merely to run riot throughout the world in the sequel. More interesting things happened that were nevertheless logical outcomes of the premise. Similarly, although the Time Patrol is a temporal police force, its series is not just cops and robbers through time.

Individual time criminals: Stane and Whitcomb in a single story; Castelar in an Exaltationist story.
Neldorians and the causal nexus: one story each.

However, the Exaltationists, encountered four times in three stories and much more sophisticated than the earlier Neldorians, provide as much temporal cops and robbers action and detective work for the Patrol as any action-adventure fiction reader could ask for.