There is some confusion about which shapes should be produced by fonts for Mongolian characters. Most letters have at least one isolated, initial, medial and final shape, but other shapes are produced by contextual factors, such as vowel harmony.
Unicode has a list of standardised variant shapes, dating from 27 November 2013, but that list is not complete and contains what are currently viewed by some as errors. It also doesn’t specify the expected default shapes for initial, medial and final positions.
The original list of standardised variants was based on 蒙古文编码 by Professor Quejingzhabu in 2000.
A new proposal was published on 20 January 2014, which attempts to resolve the current issues, although I think that it introduces one or two issues of its own.
The other factor in this is what the actual fonts do. Sometimes they follow the Unicode standardised variants list, other times they diverge from it. Occasionally a majority of implementations appear to diverge in the same way, suggesting that the standardised list should be adapted to reality.
To help unravel this, I put together a page called Notes on Mongolian variant forms that visually shows the changes between the various proposals, and compares the results produced by various fonts.
This is still an early draft. The information only covers the basic Mongolian range – Todo, Sibe, etc still to come. Also, I would like to add information about other fonts, if I can obtain them.
Update: 16 Apr 2015, The Todo, Sibe, Manchu, Sanskrit and Tibetan characters are now all done, and font information added for them. (And the document was moved to github.)