All most popular (among the user audience) browsers need to be tested. But you should pay special attention to the IE if it is included in the test suite. In IE, there are often problems that are not found in other browsers. So, in IE, it is additionally recommended to pay special attention to scalability, input areas re-focusing and JS operation.
Even if you do not have enough knowledge to assess how the markup corresponds to the standards, you can use automatic tools. We also recommend using different markup validators, for example, https://validator.w3.org/
. After analysing the result, shown by the validator, you can identify serious bugs and show them to the developers.
Sometimes validators pay attention to the most minor bugs that (let's be honest) no one will ever fix. If you create bug reports for defects of this kind, it will be more convenient to collect them into a single document and attach them to the report. All kinds of recommendations that do not have their influence on the display and operation of content can be attributed to this kind of "minor bugs".