Existing MT evaluation frameworks, including automatic metrics and human evaluation schemes such as Multidimensional Quality Metrics (MQM), are largely language-agnostic. However, they often fail to capture dialect- and culture-specific errors in diglossic languages (e.g., Arabic), where translation failures stem from mismatches in language variety, content coverage, and pragmatic appropriateness rather than surface form alone.We introduce LQM: Linguistically Motivated Multidimensional Quality Metrics for MT. LQM is a hierarchical error taxonomy for diagnosing MT errors through six linguistically grounded levels: sociolinguistics, pragmatics, semantics, morphosyntax, orthography, and graphetics (Figure 1). We construct a bidirectional parallel corpus of 3,850 sentences (550 per variety) spanning seven Arabic dialects (Egyptian, Emirati, Jordanian, Mauritanian, Moroccan, Palestinian, and Yemeni), derived from conversational, culturally rich content. We evaluate six LLMs in a zero-shot setting and conduct expert span-level human annotation using LQM, producing 6,113 labeled error spans across 3,495 unique erroneous sentences, along with severity-weighted quality scores. We complement this analysis with an automatic metric (spBLEU). Though validated here on Arabic, LQM is a language-agnostic framework designed to be easily applied to or adapted for other languages. LQM annotated errors data, prompts, and annotation guidelines are publicly available at https://github.com/UBC-NLP/LQM_MT.