Real-time detection of radar signals in a wideband radio frequency spectrum is a critical situational assessment function in electronic warfare. Compute-efficient detection models have shown great promise in recent years, providing an opportunity to tackle the spectrum detection problem. However, progress in radar spectrum detection is limited by the scarcity of publicly available wideband radar signal datasets accompanied by corresponding annotations. To address this challenge, we introduce a novel and challenging dataset for radar detection (RadDet), comprising a large corpus of radar signals occupying a wideband spectrum across diverse radar density environments and signal-to-noise ratios (SNR). RadDet contains 40,000 frames, each generated from 1 million in-phase and quadrature (I/Q) samples across a 500 MHz frequency band. RadDet includes 11 classes of radar samples across 6 different SNR settings, 2 radar density environments, and 3 different time-frequency resolutions, with corresponding time-frequency and class annotations. We evaluate the performance of various state-of-the-art real-time detection models on RadDet and a modified radar classification dataset from NIST (NIST-CBRS) to establish a novel benchmark for wideband radar spectrum detection.