Resolution with regard to images, print and displays may be quite complex.
Here are two links that talk very well about what resolution is and what standard paper sizes are:
RapidStudio's print resolution is as follows:
Digital Press: dot 200 screen
Wetlab: 300dpi or up to 640dpi on request.
Large format inkjet: 300dpi
When we talk about image resolution it's important that we talk about the resolution the image will be at it's full print size.
The image's resolution should not be less than the print resolution (at same size)
So let's take for example an image on a large format poster measuring 1 inch X 1 inch. My jpeg's resolution needs to be at least 270 pixels by 270 pixels in order for it to print optimally.
If you crop the image at all, the resolution will drop and the image will not print optimally.
As another example, If I have an image in a book (printed on the digital press) - and the image is (on the page) 2.54 cm by 5.08 cm - The jpeg file's resolution will need to be at least 200 pixels by 400 pixels.
And lastly, if I want to make an A0 poster (841mm × 1189mm) The artwork needs to be 9933 pixels x 14043 pixels. And each element in the artwork needs to be over 300dpi at it's print size too.
Out-of-focus images are not related to resolution, the software will not warn you if an out-of-focus image has been used.
If an image's pixel size has been increased, ie. if it's been enlarge in photoshop, the software's resolution warnings will be inaccurate.