Agent Mulder signs his resignation, but his signature is totally different from the signature on his badge in the intro.
The date (January 3, 1994) on Scully's medical charts when Frohike looks at them is at odds with the recent continuity. In Duane Barry (1994), on-screen titles establish Scully disappeared in early August, with a subsequent episode 3 (1994) being set sometime in November.
Byers says that Scully's (medical) "chart shows abnormal protein chains. The amino acid sequence is a combination I've never seen." The most the charts would show is the overall concentration of protein in body fluids or tissues (or the concentration of some individual marker protein) and the activities of some proteins (such as amylase and alkaline phosphatase, show on the chart). The chart would not reveal abnormal proteins and would certainly not show the amino acid sequence of any.
Byers (however expert he was in protein biochemistry) wouldn't know the sequence of every protein on sight, so it is meaningless for him to say that the sequence is one has never seen.
The Lone Gunmen describe 'branched DNA' as the cutting edge of genetic engineering. It didn't exist then or now. Even if it did, an abnormal protein sequence (which is what they were supposedly working from) would not have revealed that it was coded for by such unusual DNA.
In the hospital, Scully's mother and sister have laminated visitor badges. Family members visiting a patient don't normally need such badges.
Scully's medical chart show the concentrations various compounds or activities of enzymes. The last two columns are both labelled 'Normal', but the number ranges they show are different and only the second of the two shows units. There is no reason for two sets of 'Normal' values.
A Bible verse is inscribed on the tombstone. It says, "The Spirit is the Truth," and cites it as "1 John 5:07." The verse is actually 1 John 5:6.