Capability
While sometimes portrayed as a bumbling fool (especially in the anime series), Zenigata is a very clever and crafty adversary to Lupin. For instance in 1979's Castle of Cagliostro, Zenigata is apparently the only official to realize the heavily guarded castle has an access by way of an ignored aqueduct; converging on the area, the inspector was moments away from capturing Lupin before being called away at the worst possible time.
There are occasions when Zenigata can see through Lupin's disguises. Zenigata himself can actually pull a trick on Lupin, incarcerating the criminal at last. In most cases, Lupin regroups and escapes, often turning the detective's own trick against him. In other cases, Lupin allows himself to be captured, and Zenigata is inadvertently aiding him in his plans. While he has rarely been successful in capturing Lupin, this is more because of Lupin's resourcefulness than Zenigata's incompetence. Also, Zenigata is usually alone, while Lupin has a group of competent partners.
The inspector's excellent detective work always manages to lead him to Lupin's current location, anywhere in the world it may be. While his presence and intervention sometimes foils Lupin's thievery, he still comes up short on the capturing of his nemesis.
Still, Zenigata has a remarkable success rate in other police endeavors; he's brought numerous dangerous criminals to justice, particularly after Lupin has defeated them. This degree of success enables him to still lead the Lupin investigation, even after so many failed attempts. A highly decorated and respected professional, Lupin is the only stain on his otherwise perfect record. In 1989's Bye-Bye Liberty Crisis Zenigata has apparently "Tried and failed to arrest Lupin 738 times".
His greatest weakness is his single-mindedness; he is so intent upon catching Lupin, that he usually ignores (or fails to discover) any obstacles - even insurmountable ones - inevitably resulting in Lupin getting away. He is, however, extremely skilled - few people stand a chance when Zenigata goes after them, so his obsession with Lupin may stem from the fact that he's the only one who presents a challenge for Zenigata's talents.
Lupin is genuinely impressed with Zenigata's doggedness and skills, and has implied that he thinks it a shame he has to be a cop - under different circumstances they might have been great partners. Partly out of respect, partly out of the excitement each brings to the other, the Inspector and Lupin share an unwritten rule... neither will deliberately attempt to kill the other in their cat-and-mouse chase. Further if the Inspector is in need of help that only Lupin and gang can provide, the bunch leaps to his help without hesitation.
Zenigata is also aware that while Lupin may be a scoundrel, there are worse evils in the world, and he's willing to team up with Lupin's gang to bring down a more dangerous threat. However, this is always with the mutual understanding that he intends to arrest Lupin upon neutralization of the common foe with his loud proclamation "Lupin! You're Under Arrest!".
Read more about this topic: Koichi Zenigata