Any tips to in low-light shooting?

I find the when I shoot in Superior Auto in low-light, many times there appear a violet / bluish haze on the left side (no flash fired). I find that switching to Night Portrait or Night Mode is too much of a hassle, ESPECIALLY when the conditions constantly change like going to a different place that's brightly lit or going inside a restaurant. Also, these modes tend to have motion blur.

Now I'm thinking of Manual Mode but basically got the same results as Superior Auto (probably. I'm just not good at tinkering with the settings).

Any tips?

Thanks!