After upgrade, mostly we see the issues in UI level and the corresponding code used for building the UI. I would say the dev team need to spend most of their time is to fix all the issues to stabilize the application with the help of Pega GCS (if required). After fixing all the issues, the application should work from end to end with all validations and all. QA/UAT team contribution is also important to identify all the functionality wise issues based on their previous test cases executed in earlier version. Regression and Performance testing teams play the major role to bring the application in a good shape. I would say it is not just Dev and QA teams but is a collective effort from all stake holders who contributed in the upgrade exercise since started.
The few things which you need to know here is the deprecated rules. Like list view and all need to be taken care.
To answer this question, you need to tell which version you are currently using?
Apart from UI which mentioned in previous post, you might face some issues with the indexing as the new one is elastic search which runs on all the nodes, unlike the one we used in 6.x version. Few of the custom control may break. You need to check that as well.
Let me know your specific requirement and then only we can tell you in a better way.
Few things you need to take care before installation is to decide whether to have split schema (Best approach in upgrading production environment) or single schema, also there are common issues before/after installation are from DB perspective make sure about the database instances on your 6.2 sp2 and set datasources as per the instruction/deployment guides.
You can also visit this place https://pdn.pega.com/upgrade-center dedicated for Pega7 upgradations. There are few upgrade tools, helpful articles and forum topics covering most of the upgrade issues from 6.x to 7.x. You may have to spend some quality time there.