Internet Service Providers (ISPs) use realtime data feeds of aggregated traffic in their network to support technical as well as business decisions. A fundamental difficulty with building decision support tools based on aggregated traffic data feeds is one of data quality. Data quality problems stem from network-specific issues (irregular polling caused by UDP packet drops and delays, topological mislabelings, etc.), and make it difficult to distinguish between artifacts and actual phenomena, rendering data analysis based on such data feeds ineffective. In principle, traditional integrity constraints and triggers may be used to enforce data quality. In practice, data cleaning is done outside the database and is ad-hoc. Unfortunately, these approaches are too rigid and limited for the subtle data quality problems arising from network data where existing problems morph with network dynamics, new problems emerge over time, and poor quality data in a local region may itself indicate an important phenomenon in the underlying network. We need a new approach - both in principle and in practice - to face data quality problems in network traffic databases. We propose a continuous data quality monitoring approach based on probabilistic, approximate constraints (PACs). These are simple, user-specified rule templates with open parameters for tolerance and likelihood. We use statistical techniques to instantiate suitable parameter values from the data, and show how to apply them for monitoring data quality. In principle, our PAC-based approach can be applied to data quality problems in any data feed. We present PAC-Man, which is the system that manages PACs for the entire aggregate network traffic database in a large ISP, and show that it is very effective in monitoring data quality problems.