The leading mean-field critical behaviour of Φ44-theory is modified by multiplicative logarithmic corrections. We analyse these corrections both analytically and numerically. In particular we present a finite-size scaling theory for the Lee-Yang zeroes and temperature zeroes, both of which exhibit logarithmic corrections. On lattices from size 84 to 244, Monte-Carlo cluster methods and multi-histogram techniques are used to determine the partition function zeroes closest to the critical point. Finite-size scaling behaviour is verified and the logarithmic corrections are found to be in good agreement with our analytical predictions.