Single molecule sequencing has recently been used to obtain full-length cDNA sequences that improve genome annotation and reveal RNA isoforms. Here, we used one such method called isoform sequencing (Iso-Seq) from Pacific Biosciences (PacBio) to sequence a cDNA library from the Asian malaria mosquito Anopheles stephensi. More than 600,000 full length cDNAs, referred to as reads of insert, were identified. Due to the inherently high error-rate of PacBio sequencing, we tested different approaches for error-correction. We found that error-correction using Illumina RNA-seq generated more data than using the default SMRT pipeline. The full-length error-corrected PacBio reads greatly improved the gene annotation of Anopheles stephensi: 4867 gene models were updated and 1785 alternatively-spliced isoforms were added to the annotation. In addition, six trans-splicing events, where exons from different primary transcripts were joined together, were identified in An. stephensi. All six trans-splicing events appear to be conserved in Culicidae, as they are also found in An. gambiae and Aedes aegypti. The proteins encoded by trans-splicing events are also highly conserved and the orthologs of these proteins are cis-spliced in outgroup species, indicating that trans-splicing may arise as a mechanism to rescue genes that broke up during evolution.