As Daniel pointed out in a comment, the Book of Mormon speaks to this question on the first page:
And now, if there are faults they are the mistakes of men; wherefore, condemn not the things of God, that ye may be found spotless at the judgment-seat of Christ.
This is important to note, as people do make mistakes, and have made some significant ones with the Book of Mormon. For example, in the original printing, the word "robber" was misprinted as "nobler" as well as a handful of other typographical errors, most likely due to Oliver Cowdery's handwriting being difficult for the typesetter to read. (See "Understanding Textual Changes in the Book of Mormon" for an in-depth look at the subject.)
There also exists in the text itself a rather amusing error:
Alma 24: 19:
... and thus we see that they buried their weapons of peace, or they buried the weapons of war, for peace.
The work of writing on metal plates would not easily lend itself to erasing errors; you can just imagine Mormon cringing here as he realizes what he just wrote, and then hastily adding a bit of corrective text!
As for significant doctrinal issues, not really. The Golden Plates may not be easily accessible today, but the original English manuscript is, and it's considered doctrinally authoritative, if not necessarily textually authoritative, given that the English language was not yet standardized at the time it was written, and it was transcribed with less concern for grammar than one might hope for today. Because an original, authoritative manuscript exists to check against, the types of confusions and disagreements often seen in Biblical scholarship regarding the authenticity of various passages simply doesn't exist in Book of Mormon scholarship.