What factors should I consider when selecting a reference genome for mapping?
There are many reasons!

Let's assume you are using the Human reference genome. The latest version is hg38 or GrCh38. This came out roughly three years ago (Dec 2013). Although now these same reasons do not really apply to this particular assembly, but no other assembly comes to mind where these reasons are demonstrable. When dealing with RNA-Seq data you carry out a few common tasks.


Annotations: When a new assembly comes out, all existing annotations are standardised on the previous assembly. Take for example GENCODE, that particular links to the current version of gencode, which is now based on hg38. But, more importantly notice that they still maintain the same release for hg19/GrCh37. From my experience, it takes about 1-3 months for annotation databases to migrate to a new genome assembly after the assembly is released.
Conservation tracks: These are the tracks which take the longest to get updated. I will not post a link to the tracks here. But, here's the UCSC table browser, you can go to the comparative genomics tracks and view the conservation tracks (Phylop, Phastcons) which are available for each assembly. Again from experience, it took more than a year for these tracks to be generated for hg38. So it is just better to work on the previous assembly if you want to this particular information, because generating these tracks by self is a very tedious and computationally intensive task. 
Risks associated with unfinished genomes: This does not really deal so much with the human genome as the gain is ever smaller with each consecutive assembly. But considering a assembly which consists of 70% scaffolds, the variation between assemblies tend to be huge. For functional studies as opposed to insilico studies, it makes no sense to redo the entire analysis every time a new assembly comes out, since the insilico part of the study is the predictive pillar on which functional validations are based. Although the same does not apply to insilico studies where the results presented to the public are solely predictive.
Incoherence with existing studies: This is a major obstacle for using a newer assembly, especially applicable towards unfinished genomes, wherein the results may be widely variable and do not align with pre-existing knowledge. Of course, you may be the one who is correct but it is also possible that the variability in your results is the result of human error. Therefore, it is just better to wait for a "landmark" study to introduce the assembly to the public, allowing your study to undergo less stricter perusal and also allowing you to validate the expected variability in your results.
Pitfalls during functional analysis: For RNA-Seq analysis it is common practice to use RT-PCR for a particular gene to establish the expected expression level for that gene, which in turn will validate a successful RNA-Seq experiment bereft of shady PCR duplications and artefacts. For this particular part you would first create a primer, which validates the expected expression level of that gene. But this particular primer originates from a particular assembly. It is also possible that the region which is amplified may have shifted or changed between assemblies. So when you align your data on a different assembly from the one which was used to create the primer, you may get an unexpected expression level for that gene, as the original primer amplified an incorrect region, which got fixed in the newer assembly.


I know there are many more. But, these are the only ones which comes to mind at the moment.