Since I bought my Note 4, it has been slow to download apps... usually it is so slow it won't finish at all. I usually show 4G and three or four bars. When at home and connected to my wireless router, there is no difference. In fact, sometimes it's slower. If I persist, sometimes hours later it will say it's downloaded and then install it. I bought my Note 4 before Lollipop, and it's been the same before and after. The preferred network mode is set to global.
All other features seem to work fine. I don't have any problems with the phone.