The process of splicing messenger RNA to remove introns plays a central role in creating genes and gene variants. Here we describe Splam, a novel method for predicting splice junctions in DNA based on deep residual convolutional neural networks. Unlike some previous models, Splam looks at a relatively limited window of 400 base pairs flanking each splice site, motivated by the observation that the biological process of splicing relies primarily on signals within this window. Additionally, Splam introduces the idea of training the network on donor and acceptor pairs together, based on the principle that the splicing machinery recognizes both ends of each intron at once. We compare Splam's accuracy to recent state-of-the-art splice site prediction methods, particularly SpliceAI, another method that uses deep neural networks. Our results show that Splam is consistently more accurate than SpliceAI, with an overall accuracy of 96% at predicting human splice junctions. Splam generalizes even to non-human species, including distant ones like the flowering plant Arabidopsis thaliana. Finally, we demonstrate the use of Splam on a novel application: processing the spliced alignments of RNA-seq data to identify and eliminate errors. We show that when used in this manner, Splam yields substantial improvements in the accuracy of downstream transcriptome analysis of both poly(A) and ribo-depleted RNA-seq libraries. Overall, Splam offers a faster and more accurate approach to detecting splice junctions, while also providing a reliable and efficient solution for cleaning up erroneous spliced alignments.