duplicating midi notes

I would use the Split tool (looks like a little pair of scissors) in the Track view and cut the part you want into a seperate clip. Just split it before and after the part you want to copy. Right-click the clip, Edit>Copy then paste it wherever you want.
Note the start time of the clip in Clip Properties so you can always paste it in the exact place in the measure that you want it.
I think you can do that with the lasso thing, too; do that and right-click it and see if you can copy it.

Yeah... it sounds like you are doing a DRAG function.  You need to do as Greg said.... split before and after the points to create a new and separate clip. Highlight it...right click on it....select edit>copy. then go to the point where you want it placed...and right click again.... select paste.

What Greg says about the clip properties...also available in that same window as copy/paste... note the start time .....OR..... this can also work and is faster.... set the snap to grid setting to MEASURES. I believe that is the default setting..... when you cut and paste it is automatically done to the measure. However, that may not be precise enough so the clip properties in musical time grid will help you get the placement exact.