Conformance checking, one of the central tasks in process mining, compares the expected behavior described by a reference process model to the actual behavior recorded in an event log, with the goal of detecting deviations. Traditionally, it is assumed that the log provides a faithful and complete digital footprint of reality. However, assuming perfect logs is often unrealistic: real-life logs typically suffer from data quality issues, exposing uncertainty in their events, timestamps, and data attributes. We attack this problem by introducing a comprehensive framework for multi-perspective conformance checking dealing with uncertainty along three perspectives: control-flow, time, and data. From the modeling point of view, we consider process models formalized as Petri nets operating over data variables, and event logs presenting uncertainty at the event- and attribute-level. We cast conformance checking as an alignment problem, extending the traditional notions of alignment and cost function to deal with uncertainty along the three aforementioned perspectives. From the operational point of view, we show how (optimal) alignments can be computed through well-established automated reasoning techniques from Satisfiability Modulo Theories (SMT). Specifically, we show how previous results on data-aware SMT-based conformance checking can be lifted to this more sophisticated setting, obtaining a flexible framework that can seamlessly handle different variants of the problem. We formally prove correctness of our approach and implement it in the conformance checker cocomot. Finally, we perform a thorough experimental evaluation on synthetic and real-life logs, demonstrating the overall promising performance of our framework.