We present the results of a high-cadence photometric survey of an 11 arcmin × 11 arcmin field centred on the globular cluster M71, with the Near-Infrared Transiting ExoplanetS Telescope. The aim of our survey is to search for stellar variability and giant transiting exoplanets. This survey differs from previous photometric surveys of M71 in that it is more sensitive to lower amplitude (ΔM ≤ 0.02 mag) and longer period (P > 2 d) variability than previous work on this cluster. We have discovered 17 new variable stars towards M71 and confirm the nature of 13 previously known objects, for which the orbital periods of 7 are refined or newly determined. Given the photometric precision of our high-cadence survey on the horizontal branch of M71, we confirm that the cluster is devoid of RR Lyrae variable stars within the area surveyed. We present new B- and V-band photometry of the stars in our sample from which we estimate spectral types of the variable objects. We also search our survey data for transiting hot Jupiters and present simulations of the expected number of detections. Approximately 1000 stars were observed on the main sequence of M71 with sufficient photometric accuracy to detect a transiting hot Jupiter; however, none were found.