How do I know if this data is any good?

First, check out Where does the income data come from?

What the Census Bureau says about the American Community Survey: 

• The American Community Survey (ACS) is on the leading edge of survey design, continuous improvement, and data quality
• The nation’s most current, reliable, and accessible data source for local statistics on critical planning topics such as age, children, veterans, commuting, education, income, and employment
• Surveys 3.5 million households and informs over $675 billion of Federal government spending each year
• Visit 20,000 Group Quarter facilities and sample approximately 194,000 residents each year
• Covers 35+ topics, supports over 300 evidence-based Federal government uses, and produces 11 billion estimates each year

The ACS data are estimates collected from a sample of households and not the whole population. To assist in interpreting the reliability of the estimates, a margin of error is included for each estimate. Margins of error (MOEs) allow data users to be certain that at a given level of confidence the estimate and the actual current statistic differ by no more than the value of the MOE. The Census Bureau uses a 90% confidence level as its standard.  

Example: How many males under age 5 live in WY?

• Lower bound = 19,089 - 356 = 18,733
• Upper bound = 19,089 + 356 = 19,445

We are 90% confident the true number of males under age 5 in Wyoming falls between 18,733 and 19,445.

You can find the margins of error in the "About the Data" section at the bottom of each zip code page on Income ByZip Code website, and they are included in the zip code lists.