Online stores often utilize product relationships such as bundles and substitutes to improve their catalog quality and guide customers through myriad choices. Entity resolution using pairwise product matching models offers a means of inferring relationships between products. In mature data repositories, the relationships may be mostly correct but require incremental improvements owing to errors in the original data or in the entity resolution system. It is critical to devise incremental entity resolution (IER) approaches for improving the health of relationships. However, most existing research on IER focuses on the addition of new products or information into existing relationships. Little research has been done for detecting low quality within current relationships and ensuring that incremental improvements affect only the unhealthy relationships. This paper fills the void in IER research by developing a novel method for identifying inconsistent clusters (IC), existing groups of related products that do not belong together. We propose to treat the identification of inconsistent clusters as a supervised learning task which predicts whether a graph of products with similarities as weighted edges should be partitioned into multiple clusters. In this case, the problem becomes a classification task on weighted graphs and represents an interesting application area for modern tools such as Graph Neural Networks (GNNs). We demonstrate that existing Message Passing neural networks perform well at this task, exceeding traditional graph processing techniques. We also develop a novel message aggregation scheme for Message Passing Neural Networks that further improves the performance of GNNs on this task. We apply the model to synthetic datasets, a public benchmark dataset, and an internal application. Our results demonstrate the value of graph classification in IER and the ability of graph neural networks to develop useful representations for graph partitioning.