Usually, these "left-out" gospels (like the Gospel of Mary and the Gospel of James that you mentioned, as well as the Gospel of Thomas, the Gospel of Judas, and the Gospel of Barnabas) have a few different things in common:
1) They were not written within the lifetimes of people who would have either known Christ or known first-hand witnesses of the events they describe (as the other, canonical gospels were). Because of the proven reliability and prevalence of Jewish oral tradition, many witnesses would collaborate to attest to the truth of a statement (to make sure one faulty memory doesn't skew the facts--it's self-corrective). But since these gospels were written much, much later (sometimes 300+ years after Christ), there are no reliable sources they could possible draw from. Many weird, pagan cultural influences are easily detected in these gospels
2) They are neither prophetic, nor do they reveal any new contributions to the collective teachings of Jesus. Even if they weren't totally sketchy, they don't really contribute anything.
3) These gospels were born out of and tainted by the Gnostic movement (2nd to 4th centuries AD). Rather than keeping true to canonical Biblical teachings, they many times openly defy them--portraying salvation as something not obtained exclusively through Christ but rather by "secret" or "enlightening" wisdom or cosmic understanding that Christ came to share with mankind.
4) These gospels make unverifiable (and frankly bogus) claims with no support from other witnesses. These range anywhere from Jesus being a non-physical being who never actually died (and who hovered over the earth as to not leave footprints), to Jesus eloping with random women, to Jesus having one-night stands with his [male] disciples, to Jesus leaving the tomb with a forehead that "stretched above the clouds", being followed a talking, flying cross.
All of these claims blatantly contradict canonical scripture (that the Biblical, historical Jesus would have lived by), and fly in the face of God's plan of redemption. Many of the wilder claims made in the gnostic gospels are even contradicted by other gnostic gospels.
5) Lastly, many of these gospels (especially the Gospel of Barnabas) are riddled with numerous lingual, historical, geographical and cultural errors--rendering them completely untrustworthy, even when theology is taken out of the equation.
Hope that helps!