Is there such a thing as setting too strong an intent?
There can be, especially in cases where it becomes overkill. The key with setting and applying intent is to gage the situation; use the intent and ratchet up the volume with will if you need to.
For example, let's say that you intend for someone to help you with something, but you over reach. Instead of just helping you, they become a pest you can't get rid of. Then you have to recap the old intent and actually replace it with a new one to calm the situation. It's so hard to learn to handle intent well, that once you actually start getting results, you have a tendency to over do. It's like you have a new hammer, and now every problem becomes a nail. I would set an entirely new intent, but also try to calm the situation as well.
So, would one look to see if any intent is in the way before setting one?
I do. I try to make sure that my intent is clear and will have a straight line to the goal I've set. If it doesn't, then I try to set smaller intents to gain a better shot. For instance, you want to take a trip overseas, but to set the intent in motion for that you look and see there are other intents which must be either overcome or removed, so you work on those first and then set your intent and ignite it. You can also set intent that will act with and on other intents, but change in nature as they go to act in a final way on an ultimate goal. Subtle is always better, though, and easier to deal with. Plus, it keeps people from staring at you. You can use the energy in other people's intents to aid your own - setting your intent in a way that allows for the connection, use, reformulation and movement past the intents it is interacting with.