From the point of view of identifying people quickly, with the full, historical coercion level of highly organized states, up to, but not including, development of photographic imaging and telegraphs, c 1860s, how much did our lack of non-photographic "suspect description" or broadcast technologies affect historically known incidents of suspect apprehension successes or failures?
If you were a serial killer/military spy/person blackmailing the hereditary monarch about her propensity for picking her august nose, could you have reasonably slipped out, after being fingered, in the 1500s? In the 1800s? Did it happen?
Something like say Mata Hari slipping out because the description was easy to mess up? Would Napoleon have managed to arrest a known spy?
As you gradually got out of your immediate area of police notoriety, wouldn't you very quickly be able to slip ahead of any organized search?
To be clear, consider anything more recent than railroad and/or telegraph technology out of scope here.