High-statistics measurements of differential cross sections and recoil polarizations for the reaction γp→K+Σ0 have been obtained using the CLAS detector at Jefferson Lab. We cover center-of-mass energies (√s) from 1.69 to 2.84 GeV, with an extensive coverage in the K+ production angle. Independent measurements were made using the K+pπ-(γ) and K+p(π-, γ) final-state topologies, and were found to exhibit good agreement. Our differential cross sections show good agreement with earlier CLAS, SAPHIR, and LEPS results, while offering better statistical precision and a 300-MeV increase in √s coverage. Above √s≈2.5 GeV, t- and u-channel Regge scaling behavior can be seen at forward and backward angles, respectively. Our recoil polarization (PΣ) measurements represent a substantial increase in kinematic coverage and enhanced precision over previous world data. At forward angles, we find that PΣ is of the same order of magnitude but opposite sign as PΛ, in agreement with the static SU(6) quark model prediction of PΣ≈PΛ. This expectation is violated in some mid- and backward-angle kinematic regimes, where PΣ and PΛ are of similar magnitudes but also have the same signs. In conjunction with several other meson photoproduction results recently published by CLAS, the present data will help constrain the partial-wave analyses being performed to search for missing baryon resonances.