Yes, find a way to fix this. You're not the only one getting these errors, your users will as well.
The indication icon in the URL-bar will show a faulty connection icon because not everything is https, thus it's not 100% safe (assuming full https is 100%).
This will scare off people.
- You should try to link to
//www.example.com/img.jpg, without http(s)
- If no https variant available, just download the image and show your own version
- Try to convince the other site to go to https or at least get a 10$/yr certificate to allow basic https
Don't forget to add a "save external resource to file/session/cookie and next load, load that instead of a new
file_get_contents()". You will increase your own bandwith (you make the server download it from another server, and upload it to your users browser, two steps that where not there). This trick will limit bandwith abuse.