The following code fails:

var doc = new BsonDocument() { AllowDuplicateNames = true };

doc.Add("x", 1);

doc.Add("x", 2);

var doc2 = new BsonDocument(doc); // throws

This is because the parameter is treated as an IEnumerable<BsonElement>. This can be fixed by adding a new constructor:

/// <summary>
/// Initializes a new instance of the BsonDocument by coping elements from another BsonDocument.
/// </summary>
/// <param name="document">The document whose elements will be copied</param>

public BsonDocument(BsonDocument document)
{
  if (document == null)
  {
    throw new ArgumentNullException("document");
  }

  _allowDuplicateNames = document.AllowDuplicateNames;
  AddRange(document);
}

This could be ambiguous if somebody tried to pass a RawBsonDocument or LazyBsonDocument, so two additional constructors may be useful:

/// <summary>
/// Initializes a new instance of the BsonDocument by coping elements from a LazyBsonDocument.
/// </summary>
/// <param name="document">The document whose elements will be copied</param>

public BsonDocument(LazyBsonDocument document) : this((BsonDocument)document) { }

/// <summary>
/// Initializes a new instance of the BsonDocument by coping elements from a RawBsonDocument.
/// </summary>
/// <param name="document">The document whose elements will be copied</param>

public BsonDocument(RawBsonDocument document) : this((BsonDocument)document) { }