Firstly before applying paint to a newly plastered wall the golden rule here is making sure the plaster is completely dry.
I would always recommend that you give the walls a good rub down with some sandpaper first. Some in the trade recommend that you use a primer to help seal the walls before painting them.
Another method widely used is to use quality emulsion paint as a primer and first coat. When this dries and you still see patches again lightly sandpaper now apply the second coat of paint to the wall. This second coat should seal the entire surface. To get the professional finish you may be required to apply a third coat.
Here are some of the different types of paints to use, a matt, vinyl matt, vinyl silk, vinyl soft sheen or any other type of emulsion?
Just to note sometime when you use a roller or brush where the paint overlaps some sections can look lighter because they are smoother and have more paint applied to them.