Since this is a response to the Skeptic's Annotated Bible's What the Bible Says about Believers I have decided only to address what they have actually said rather than add anything to it regarding what I personally think the Bible says about believers.
Mark 16:17-18 are generally regarded as spurious scriptures. Mark 16:9-20 consists of two conclusions, one short and one long. They seemed to have been added on later, since the earliest manuscripts don't include them.
The Greek Codex Alexandrinus, and Ephraemi rescriptus from the fifth century C.E., as well as the Greek and Latin Bezae Codices from the fifth and sixth centuries C.E., Jerome's Latin Vulgate c. 400 C.E., Curetonian Syriac, Old Syriac and Syriac Peshitta, Christian Aramaic both from the fifth century C.E. add the long conclusion, but the Greek Codex Sinaiticus and Vatican ms 1209, both from the fourth century C.E. as well as the Cinaitic Syriac codex from the fourth and fifth century C.E., and Armenian Version from the fourth to thirteenth century C.E. omits them. It would seem, especially when examining the context, that these verses were added sometime during this period.
It is true that many of the things referred to in those verses were a part of the early Christian experience and the uninformed Bible critic tends not only to exaggerate them but also to overlook their temporary usefulness. This comes from some of the strange modern day charismatic Christian sect's misapplication of the Bible where these sorts of things happened. The apostle Paul, for example, was bitten by a poisonous viper with no ill effect because he had a job to do and God's Holy Spirit was going to see that it was done when it needed to be done. Not so that in the future anyone claiming to be a Christian could dance around holding poisonous serpents to impress people. (Acts 28:3-6 / 1 Corinthians 12:7-11)
Speaking in tongues was something that was used at Pentecost 33 C.E. but was not something that all Christians were capable of understanding or performing. (1 Corinthians 12:29-30) It is important to recognize that when any of these works that were recorded in the Bible after Pentecost took place either one of the 12 apostles or Paul was present. After they had all died these things evidently ceased to occur because they were no longer needed to demonstrate that God was now using the Christian congregation instead of the Jewish congregation.
At Luke 10:19 Jesus sends his disciples out among scorpions and serpents, which was meant to be a warning against all sorts of injurious things, including but not limited to a literal reference to actual scorpions and serpents. The nature of the political and religious scene at the time would have been something to consider as well. (Compare Deuteronomy 8:15 / Ezekiel 2:6)
The Hebrew word for scorpion is aqrav, the Greek scorpios. The SE frontier of Judah, which lies SW of the southern edge of the Dead Sea is known as Akrabbim (Numbers 34:4), which means scorpions. The same Hebrew term akrabbim is used for "scourges" at 1 Kings 12:11-14 and 2 Chronicles 10:11-14 because the instrument of punishment mentioned was probably one with sharp points.