Elhin Grade 312

The grade grade 312 Elgin movement is a 16 size, 15 jewel, design.

This one was made about 1914.  

This is a hunter case movement installed in an open-face case. That places the winding arbor at 3:00. These are commonly referred to as side-winders.

There is nothing necessarily "incorrect" about this, it's quite common with antique American watches.

Most American watch companies sold bare movements only, and in most instances did not even make watch cases. The watch cases were selected and purchased separately by the original buyer. So the case type watches are found with is really a matter of personal preference, and likely price and availability too.