How can I save images that are on an iPhone but not in iCloud? I have an iPhone 4 with 1275 photos in the "all Photos" folder. 
In the connected iCloud only 114 are shown.
As we wish to replace the phone with a newer one we would like to save all 1275 images from the phone.
Connected to iTunes about 600 are shown. All images previous to March 2015 are not shown in iTunes. 
Those image show a small exclamation mark in the bottom corner when looked at it on the iphone.
We tried connecting to Dropbox without success. Also sending the images via email.

What can we do to save the images from the old phone?
Try the following: 
Connect your iPhone with your Mac and start "Image Capture" for importing photos.

In general, the circled explanation mark indicates that those photos have not been loaded from iCloud. It may download with network connection (mostly Wi-Fi only). If there are no photos on iCloud this might be because of file corruption on iCloud. 

Also, iOS support for iPhone 4 stopped with iOS 7.1.2 - iCloud Photo library needs iOS 8.3 or newer. Your device therefore only supports iCloud My Photo Stream which only contains your newest pictures. There is no chance for your full library to be synced with iCloud.
(This does not count for iPhone 4s which supports iOS 9.3.5)

One last thing: Make sure photos are not indicated as "Transferred from Mac" (transferred photos can not be saved on any other Mac as the original source and won´t be shown on your current Mac).

Hopefully you´ll be able to access your photos. I hope these information may help you to understand your situation. Good luck!