Conversational emotion recognition represents an important machine-learning problem with a wide variety of deployment possibilities. The key challenge in this area is how to properly capture the key conversational aspects that facilitate reliable emotion recognition, including utterance semantics, temporal order, informative contextual cues, speaker interactions as well as other relevant factors. In this paper, we present a novel Graph Neural Network approach for conversational emotion recognition at the utterance level. Our method addresses the outlined challenges and represents conversations in the form of graph structures that naturally encode temporal order, speaker dependencies, and even long-distance context. To efficiently capture the semantic content of the conversations, we leverage the zero-shot feature-extraction capabilities of pre-trained large-scale language models and then integrate two key contributions into the graph neural network to ensure competitive recognition results. The first is a novel context filter that establishes meaningful utterance dependencies for the graph construction procedure and removes low-relevance and uninformative utterances from being used as a source of contextual information for the recognition task. The second contribution is a feature-correction procedure that adjusts the information content in the generated feature representations through a gating mechanism to improve their discriminative power and reduce emotion-prediction errors. We conduct extensive experiments on four commonly used conversational datasets, i.e., IEMOCAP, MELD, Dailydialog, and EmoryNLP, to demonstrate the capabilities of the developed graph neural network with context filtering and error-correction capabilities. The results of the experiments point to highly promising performance, especially when compared to state-of-the-art competitors from the literature.