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Replaced the digitizer screen successfully on an iPhone 6, however, during reassembly a small blue tinted piece of plastic...

Successfully replaced the Digitizer Screen assembly, but there is an opaque crescent shaped halo around the outer edges of...

You can save a few bucks if you opt for the digitizer screen alone rather than the complete assembly. That means you will transfer a few small components, so a little more work and slightly increased risk of damage from disassembly/reassembly, but also means those components will be genuine Apple. There have been some reports of issues with mic volume, etc. on the complete assembly replacements. My replacement went pretty smoothly.

Probably just have the cables out of order. Check the posts above.

This is good advice, and usually the problem people experience here. There is a very specific way the ribbon cables are layered, and if not correct when reassembled, the reach of the cables will cause you to assume which cable goes where and to try to insert the wrong plugs into the wrong sockets. Please do not try to force them. If they don't snap in easily, examine them closely, and you'll see the plugs and sockets are slightly different sizes, with one wider than the other. Better to take care to note how the cables layer during disassembly, or perhaps mark them to avoid this frustration on reassembly.