You're on the right lines with the idea about it being acceptable some times and not others, look at yourself in the third person in the different places.
For example:
A Bar - Bars are social places you wouldn't look out of place chatting to many different people there
A town square - Great place for an intial approach but as you quite rightly put it you would look "weird" going between the different groups of people.
Acting like you're off in a hurry somewhere is great as a false time constraint but don't say that then open a set like 10 yards down the road of something, you may well take a beating from the bitch stick
Basically a lot of it is common sense, if you know that you're not acting like a weirdo then the feeling in your stomach can just be down to nerves (or that chicken burger from the shop last night) and giving it a temporary rest for the day could be a good call..
If, HOWEVER, you can clearly see that from the outside you are coming across as a complete and utter weirdo then that feeling in your stomach is a warning from your body to change the way you're going about things.
Sorry if this response comes across a bit incoherent, it's been a long day for me