The length of Vincent D'Onofrio's beard varies back and forth from bushier to shorter throughout the episode.
The lab technician says she found traces of Isobutylene on the glass fragment. Isobutylene is a highly toxic, flammable gas at room temperature which can only be liquified under high pressure. It is used to manufacture isooctane a high octane aviation fuel and has many other uses in manufacturing. Even if the glass somehow came into contact with it, it would evaporate away almost immediately leaving no trace for the lab technician to find.
The lab tech says the glass "could be from a window, a bottle, a vase..." - these three things us totally different sorts of glass, and can easily be distinguished.
When questioning the parents about the kidnapping of their baby Eames asks them if they were sure they locked the door when they left the room. Yet Eames should know that hotel room doors, especially ones with modern electronic key-card locks, will automatically lock each time the door closes.