Solution or Workaround
Summary
ArcView does not display all of the features of a DGN file.
Cause
Microstation drawings may contain many different feature classes known as elements. Examples of element types are line string, text, curve, textnode, cell, etc. Each instance of an element has a series of properties associated with it. Examples of properties are color, line type, level, and class. ArcView supports many Microstation elements, but only if the class property is 'Primary' (Class code = 0). This is the default class for all elements in a drawing. If the class property is set to anything else, i.e. construction, dimension, then that feature will not display in ArcView.
Solution
Reassign those features to the Primary Class. This must be done inside of Microstation. Consult the Microstation documentation for information on how to do this. A potential workaround to reassigning the elements to the Primary Class is to convert the DGN to a coverage using the IGDSARC command at the ARC prompt. ArcInfo supports the following Classes:
0 - Primary
1 - Pattern element
2 - Construction element
3 - Dimension element
4 - Primary rule element
5 - Linear patterned element
6 - Construction rule element