I believe the issue is with the Content-Type. In the first block below contains the headers for the failing link. You can see it is listed as image/jpg/jpeg.
HTTP/1.1 200 OK
Content-Length: 137496
Content-Type: image/jpg/jpeg
Content-MD5: zPyz4CSRnPhQtW7PT1w9LQ==
Last-Modified: Wed, 03 Feb 2016 11:06:14 GMT
ETag: 0x8D32C8A086B77F5
Server: Windows-Azure-Blob/1.0 Microsoft-HTTPAPI/2.0
x-ms-request-id: e25e0d4c-0001-0049-5ff0-5ea774000000
x-ms-version: 2009-09-19
x-ms-lease-status: unlocked
x-ms-blob-type: BlockBlob
Date: Thu, 04 Feb 2016 02:08:52 GMT
The response headers for the working link have a Content-Type as image/jpeg.
HTTP/1.1 200 OK
Content-Length: 1689160
Content-Type: image/jpeg
Content-MD5: iAhgwODEpi7EaTAyUCMY1Q==
Last-Modified: Mon, 01 Feb 2016 08:18:24 GMT
ETag: 0x8D32AE0413D02B6
Server: Windows-Azure-Blob/1.0 Microsoft-HTTPAPI/2.0
x-ms-request-id: 9792c6d9-0001-0045-2cf0-5e4985000000
x-ms-version: 2009-09-19
x-ms-lease-status: unlocked
x-ms-blob-type: BlockBlob
Date: Thu, 04 Feb 2016 02:06:50 GMT
If you want to update the Content-Type of a lot of files at once, you can look at the example in the answer for this SO link at Set Content-type of media files stored on Blob
If you're wondering about the difference between jpg and jpeg, you can look at this SO link JPG vs. JPEG image formats