I'm playing MDK (the first one), am a few missions in, and enjoying it. However, I am not a fan of time limits, and I notice that you can beat the missions without completing them within the time limit. It just says you failed to save the city and takes you on to the next mission.

Is there any disadvantage in failing the time limits, or advantage in adhering to them? Can I beat the whole game, get all the weapons, etc., and get the best ending without bothering about the time limits?

As far as I have observed, failing to save a city makes absolutely no difference. Also, from level 2 onwards, you should have more than enough time for each city. Only level I found myself rushing was Level 1.

I played this game for the first time yesterday. The time limit is only there for bragging rights, really. If you complete the missions within the time limit then you saved that city, but if the time runs out then all you get is a message to say that the city was destroyed and the game continues. There is no difference to the ending either as there is only one ending.

In fact, to be honest, certainly on easy, the time limit is nothing. On my first run I only failed on the last city. However, on my second run through the game (yes, I played it through twice to completion in one session) being as I knew where to go and what to do I was able to race through the game seriously quickly and was never in danger of running out of time.