I don't have that much experience with this, but  I also had these differences in GFP expression. In my hands the ones with the brightest GFP expression had multiple integration sites. Are your target cells a cell line? In the end I went for clonal expansion of my GFP positive cells- I selected GFP mid expressing cells and then sorted them as single cells and expanded 3 different lines per vector to get clonal lines. 

I also suspect that it is a matter of num of integration sites. when i started working with GFP viruses I was amazed with the amounts of false positives after selection. I just facs sort the cells to avoid working with multiple clones.

What does your vector have other than GFP?  If there's a protein for overexpression or an shRNA for knockdown, there's a chance that the overexpression or knockdown is detrimental to the cells.  This can lead to a wide range in GFP expression levels as the cells try to survive the insult. 

Puromycin selection remains efficient than GFP in many lenti viral selection studies. Recent lenti viral vectors have both GFP and Puromycin selection. You didn't mention whether your vector has puromycin selection gene or not. If your vector has only option for GFP, then even after sorting cells for GFP+ve, there are many instances where the promoter gets methylated and remains inactive. This was observed in puromycin resistant cells also. Once the promoter gets methylated, as we know they don't express the gene of interest i.e. shRNA or over-expression gene. 

I have found that GFP is expressed at very different levels if my MOI is too high. This makes it possible for muliple integration in some cells while others are left with a single insertion. Lowering to MOI seems to solve this problem somewhat. If this problem is still seen, it's probably a good idea to FACS sort after puro selection.