In Cognitive Radio Networks (CRNs), spectrum sensing is performed by secondary (unlicensed) users to utilize transmission opportunities, so-called white spaces or spectrum holes, in the primary (licensed) frequency bands. Secondary users (SUs) perform sensing upon arrival to find an idle channel for transmission as well as during transmission to avoid interfering with primary users (PUs). In practice, spectrum sensing is not perfect and sensing errors including false alarms and misdetections are inevitable. In this paper, we develop a continuous-time Markov chain model to study the effect of false alarms and misdetections of SUs on several performance measures including the collision rate between PUs and SUs, the throughput of SUs and the SU delay in a CRN. Numerical results indicate that sensing errors can have a high impact on the performance measures.