Executing the following queries I was expecting the same result but apparently they are dealt differently:

2 scenarios

• matching

  nair(mongod-2.7.0-pre-) test> db.system.namespaces.find({ name:/\$/} )
  {
    "name": "test.data.$_id_"
  }
  {
    "name": "test.difference.$_id_"
  }
  {
    "name": "test.posts.$_id_"
  }
  {
    "name": "test.kunal.$_id_"
  }
  {
    "name": "test.maha_example.$_id_"
  }
  

  has the same result has using $regex operator

  nair(mongod-2.7.0-pre-) test> db.system.namespaces.find({ name:{ $regex: "\\$"}} )
  {
    "name": "test.data.$_id_"
  }
  {
    "name": "test.difference.$_id_"
  }
  {
    "name": "test.posts.$_id_"
  }
  {
    "name": "test.kunal.$_id_"
  }
  {
    "name": "test.maha_example.$_id_"
  }
  

• not matching query

  nair(mongod-2.7.0-pre-) test> db.system.namespaces.find({ name: {$not: /\$/}} )
  {
    "name": "test.system.indexes"
  }
  {
    "name": "test.data"
  }
  {
    "name": "test.difference"
  }
  {
    "name": "test.posts"
  }
  {
    "name": "test.kunal"
  }
  {
    "name": "test.maha_example"
  }
  {
    "name": "test.system.profile",
    "options": {
      "capped": true,
      "size": 1048576
    }
  }
  

  But using $regex operator fails

  nair(mongod-2.7.0-pre-) test> db.system.namespaces.find({ name: {$not:  { $regex: "\\$"}}} )
  error: {
    "$err": "Can't canonicalize query: BadValue $not cannot have a regex",
    "code": 17287
  }
  

Is this the expected behaviour ? and if so why ?

Looking deeper in the code I can also see the following comment:
mongo/db/matcher/expression_parser_tree.cpp:103

...
         // TODO: this seems arbitrary?
         // tested in jstests/not2.js
         for ( unsigned i = 0; i < theAnd->numChildren(); i++ )
             if ( theAnd->getChild(i)->matchType() == MatchExpression::REGEX )
                 return StatusWithMatchExpression( ErrorCodes::BadValue, "$not cannot have a regex" );
...

and looking int the jstests it makes even less sense:

jstests/core/not2.js

  49 check( {i:{$not:/a/}}, "b" );
  50 check( {i:{$not:/(a|b)/}}, "", 0 );
  51 check( {i:{$not:/a/,$regex:"a"}}, "", 0 );
  52 check( {i:{$not:/aa/}}, "a", 2 );
  53 fail( {i:{$not:{$regex:"a"}}} );
  54 fail( {i:{$not:{$options:"a"}}} );