With this type of secretive research there is always the problem of the researcher "going native" (thereby ceasing to observe the group objectively). The ability to record data is also a major problem, since the researcher cannot openly record  this information. This means the reader of the research has to take it on trust the researcher saw what they claimed to see within the group - which involves questions of both data reliability and validity that cannot always be easily answered by the covert researcher. Finally, of course, there may be general ethical questions about this type of research...