The plugin either uses it's own template (ecp-page-tempalte.php or ecp-single-template.php) if you have the Default Events Template selected in Events > Settings or it will use your theme's page.php template if you have selected Default Page Template or other page template in your theme...
So, if you're using our templates for event pages, it's likely there's some markup that's not being include necessary for your theme's layout. It could be a similar situation even if you are using the Default Page Template or other page template. Bottom line is you need to take a look at the markup and CSS applied on non-plugin pages and compare with that on plugin pages (calendar, single events, etc.) and see what's missing.
Can you provide a link to your website so I can take a quick look? What template do you have selected from the above options?