We've done RNA-Seq on 32 breast tumor RNAs; for the most part the RIN values were more than adequate for RNA-Seq. Strand-specific libraries were made and paired-end 100 bp reads performed. Our Bioinformatics core gave us the QC report for RNA-Seq analysis of the RNAs. They told us that the data quality is not very good based on the relatively low % mapped reads (<80%) and the significant drop off in read quality after 60 bp. All 32 samples looked similar so I doubt the problem is quality of the RNA samples. Does this result suggest that there was some systematic problem with the library preparation and/or sequencing.
In general, I would say >80% alignment is ideal (and realistic to achieve, in most cases), but <80% alignment isn't necessarily horrible. Less than 50% or 20% is another story.
The significant drop off isn't good, but I can typically get decent gene-level counts with single-end 40-bp reads. So, you'll exceed that if you just trim off the last 40 bp. I would also recommend recalculating the alignment percentage after trimming the reads - I would expect the alignment percentage to increase when focusing only the high-quality portion of the reads.
How many reads do you have per sample? You should have at least 10 million for differential expression (single-end count is OK in most cases). 20-40 million paired end is good for splicing analysis.
I haven't worked with strand-specific data before. Perhaps that is a factor? Otherwise, I think there is still potential for the data to be usable.
You should also consider the expertise of those who mapped the read data. Is it possible that mapping wasn't done properly... for instance, would removal of poor quality trailing bases from the reads, contaminating adapter sequences, etc. have improved the mapping?