Multiword expressions (MWEs) refer to idiomatic sequences of multiple words. MWE identification, i.e., detecting MWEs in text, can play a key role in downstream tasks such as machine translation, but existing datasets for the task are inconsistently annotated, limited to a single type of MWE, or limited in size. To enable reliable and comprehensive evaluation, we created CoAM: Corpus of All-Type Multiword Expressions, a dataset of 1.3K sentences constructed through a multi-step process to enhance data quality consisting of human annotation, human review, and automated consistency checking. Additionally, for the first time in a dataset of MWE identification, CoAM's MWEs are tagged with MWE types, such as Noun and Verb, enabling fine-grained error analysis. Annotations for CoAM were collected using a new interface created with our interface generator, which allows easy and flexible annotation of MWEs in any form. Through experiments using CoAM, we find that a fine-tuned large language model outperforms MWEasWSD, which achieved the state-of-the-art performance on the DiMSUM dataset. Furthermore, analysis using our MWE type tagged data reveals that Verb MWEs are easier than Noun MWEs to identify across approaches.