Hello Jeeva
Your example is a little misleading, as it allows for ellipsis, i.e.
1. We have been to the local supermarket and (have) bought some stationery, etc.
To test for whether we can mix the present perfect with the simple past, we need to use an irregular verb for the second verb. Here's an example. First, a present perfect in both clauses, as in #1:
2. We've been to Buckingham Palace and (have) seen the Queen.
Now compare:
3. We've been to Buckingham Palace and saw the Queen.
To my ears, this is a little awkward; it would be better to use either #2, or to write:
4. We've been to Buckingham Palace; we saw the Queen.
MrP