We're considering installing MySQL on the same database server that has been running MS SQL Server. From my research there are no technical issues running both concurrently, but I am worried that the performance will be affected. Is by default SQL Server set up to use all available memory for example? What should I look out for? Thanks
Your performance will be affected more or less since both systems are competing for machine resources and it's up to you to decide whether this performance hit is acceptable or not. This is too broad a question to be answered in an online community since it greatly depends on your specific usage in your environment.
Generally speaking you're better off having them on dedicated machines but ymmv...
On the SQL server side, there is minServerMemory and maxServerMemory to control the memory consumption.
The real question is more the type of applications which use the database systems. Is this more OLTP or more BI. The other obvious problem might come from the disks/storage facilities which you use for the databases.