The negative consequences of this are a potential loss of public control over the law enforcement community and a reduction in standards as private companies try to make profit without much attention to other considerations.
Private companies, quite rightly, are most concerned with seeking profit. If private companies run law enforcement services, they might seek to achieve profit at all costs. This might lead to a decline in the level or the quality of vital services that the public depends upon for its safety. In order to make profit, the firms might cut back on expenses in ways that degrade their ability to provide a good service.
In addition, private companies would be farther out of the control of the public. Government agencies are easier for the public to control. If law enforcement were privatized, it might be harder for the public to force the companies to act in ways that are consistent with what the public wants.