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Ai
What difficulty level were you playing when these situations occurred? The AI is given more of an advantage by decreasing your advantages when difficulty increases - that's what makes the game more difficult. I think this is not so much an issue with Civ3 as it is with AI in general. This type of situation, spearmen defeating battleships and the like, has been happening since Civ1. It has improved greatly since then and is a rare occurrence on games that I play on Civ3.
Another situation to consider is that more than just the hitponts for a unit is considered in a battle. There are terrain factors, empire power, empire morale, and historic factors that must be considered for the probability of a victory. Example, I had 2 veteran musketmen defending an isolated city defeated by an Aztec archer on a mountain who didn't loose a single hitpoint. Of course this led me into a rant of unrealistic AI's, game play, etc. but calmed down and realized that this was a realistic defeat. I ended up gaining the city back culturally anyway, woohoo!
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