It is currently not possible to handle field names with dollar signs in aggregation (e.g. in $project). However, there are cases where this is perfectly valid, e.g. when trying to aggregate over system.profile, where queries and all their operators are treated as data.

For example, if system.profile contains:

{"$query" : { "date" : { "$gte" : ISODate("...") } } }

There is no way to project the $gte field. The only workaround, currently, seems to be to dump the collection to BSON or JSON, and replace "$gte" with "dgte" or something similar, then aggregate over the modified collection.