Wireless mesh network (WMN) has been deployed as a key and progressing technology all around the world to provide the end-to-end users with high quality of service. Regarding of its major design concern as network throughput, WMN has been evolved based on multi-channel multi-radio strategy to make simultaneous transmissions possible. The advent of this significant improvement has introduced other challenging issues such as channel assignment (CA). Its core strategy applied in multi-radio multi-channel WMNs to promote achievable capacity using properly mapping the available channels to the radio interfaces. Although, in recent years, there are a number of research studies on CA's improvement, there are some security drawbacks that should be addressed. Most of CA schemes assume all nodes involved in CA techniques are trustworthy. This unrealistic assumption and misbehavior of those nodes makes the network susceptible to various security attacks which lead to performance degradation. This paper presents an in-depth survey of the CA's attacks as well as detection or prevention mechanism found in the literature. The attacks are classified into two groups: attacks imposed by the malicious neighbor as well as by the assigner or the assignee. In addition, a comparative and analytical discussion is provided on current solutions and their open problems. According to conducted analysis, the current knowledge gap leading to most of these attacks is lack of accurate verification because of implicit trust in nodes in CA procedure. Although, there are some research studies proposing kinds of case-specific verification, they cannot close the gap properly, and there is a need to comprehensive approach. Finally, reviewing state-of-the-art of related works shows, there are more possible attacks such as collusion or multistage attacks that have not taken into account so far.