I don’t thing there is configured limit for tags amount. But there is warning about amount of tag rules inside tag definition. When you have more than 15 tag rules Dynatrace is showing you warning about performance.
As well, you have to remember that your browser has to render views properly. If you will add 1000 tags to single entity, browser may freeze on every page load. As well interface will break.
We have large environments with thousands of hosts and we never have more than 10-12 tags per entity.