Despite remarkable progress in text-to-SQL semantic parsing in recent years, the performance of existing parsers is still far from perfect. At the same time, modern deep learning based text-to-SQL parsers are often over-confident and thus casting doubt on their trustworthiness when deployed for real use. To that end, we propose to build a parser-independent error detection model for text-to-SQL semantic parsing. The proposed model is based on pre-trained language model of code and is enhanced with structural features learned by graph neural networks. We train our model on realistic parsing errors collected from a cross-domain setting. Experiments with three strong text-to-SQL parsers featuring different decoding mechanisms show that our approach outperforms parser-dependent uncertainty metrics and could effectively improve the performance and usability of text-to-SQL semantic parsers regardless of their architectures.