Occurrence

MapInfo tab files can contain different object types. When exporting to ESRI ArcGIS Shape files, this will fail as they can only contain 1 type of object. So you need to split the files based on the object type.

Solution

You can use Discover's Query>Text>Split by Attribute. Then select the field obj. This is a hidden field you don't normally see in Mapinfo, which contains the object type.

Hit OK and it will save to separate tables.

You may also wish to display this information in the Browser view -

1) Open a new browser for the vector layer
2) Right click in the browser and select Pick Fields
3) From the Fields list, select Expression..
4) In the Expression Window select from the Columns drop-down list 'obj'
5) OK and close the Pick Fields dialog. 

There will be a new column displayed in the browser that describes the object type for each row/object. You can filter or query to browser and table also on this field name.