Exim 4.72 and earlier allows local users to gain privileges by leveraging the ability of the exim user account to specify an alternate configuration file with a directive that contains arbitrary commands, as demonstrated by the spooldirectory directive.
Heap-based buffer overflow in the stringvformat function in string.c in Exim before 4.70 allows remote attackers to execute arbitrary code via an SMTP session that includes two MAIL commands in conjunction with a large message containing crafted headers, leading to improper rejection logging.
Setup script used to generate configuration can be fooled using a crafted POST request to include arbitrary PHP code in generated configuration file.