What are the black marks on a paper birch tree?

Answer 1

The dark lines on birch bark are called "lenticels".
A lenticel is a spongy area present in the cork surfaces of the stems, roots, and other parts of vascular plants. It appears on the surface as a lenticular (lens-shaped) spot, which acts as a pore. These structures allow for the exchange of gases between the internal tissues and atmosphere to occur across the periderm, which would otherwise prevent this exchange of gases. The name lenticel, derives from its lenticular shape.
http://en.wikipedia.org/wiki/Lenticel

Those marks are just part of the Birch's bark as it ages. The bark, brown at first, whitens and peels into paper-thin layers, marked by narrow horizontal lines.
http://plants.usda.gov/java/largeImage?imageID=bepa_005_ahp.tif
http://www.oplin.org/tree/fact%20pages/birch_paper/birch_paper.html

The thin, papery bark becomes pure white with age, marked by many pores or “lenticels”
http://www.dnr.state.mn.us/trees_shrubs/deciduous/paperbirch.html

"The bark also has dark brown "eyes," or branch scars, scattered on the trunk and small horizontal lines and irregular color with white and yellow patches."
http://www.dnr.state.wi.us/org/caer/ce/eek/veg/trees/paperbirch.htm

Good Luck! Hope this is helpful.

Answer 2

This may be normal, as it is getting too much water. But check for infestation of insects, Birch bores. Do not worry but it is very close to your House. If possible top it off just below the lowest point of the roof, to avoid the mess and the other problems.