When attempting to upgrade the version of Jenkins from 1.624 to 1.625:
http://mirrors.jenkins-ci.org/war/ does not contain the proper war file.
I think there was a very similar defect with the previous version....

jenkins.war
Failure -
hudson.util.IOException2: Failed to download from http://updates.jenkins-ci.org/download/war/1.625/jenkins.war (redirected to: http://mirrors.jenkins-ci.org/war/1.625/jenkins.war)
at hudson.model.UpdateCenter$UpdateCenterConfiguration.download(UpdateCenter.java:797)
at hudson.model.UpdateCenter$DownloadJob._run(UpdateCenter.java:1148)
at hudson.model.UpdateCenter$DownloadJob.run(UpdateCenter.java:1126)
at java.util.concurrent.Executors$RunnableAdapter.call(Unknown Source)
at java.util.concurrent.FutureTask.run(Unknown Source)
at hudson.remoting.AtmostOneThreadExecutor$Worker.run(AtmostOneThreadExecutor.java:110)
at java.lang.Thread.run(Unknown Source)
Caused by: java.io.FileNotFoundException: http://mirrors.jenkins-ci.org/war/1.625/jenkins.war
at sun.reflect.NativeConstructorAccessorImpl.newInstance0(Native Method)
at sun.reflect.NativeConstructorAccessorImpl.newInstance(Unknown Source)
at sun.reflect.DelegatingConstructorAccessorImpl.newInstance(Unknown Source)
at java.lang.reflect.Constructor.newInstance(Unknown Source)
at sun.net.www.protocol.http.HttpURLConnection$10.run(Unknown Source)
at sun.net.www.protocol.http.HttpURLConnection$10.run(Unknown Source)
at java.security.AccessController.doPrivileged(Native Method)
at sun.net.www.protocol.http.HttpURLConnection.getChainedException(Unknown Source)
at sun.net.www.protocol.http.HttpURLConnection.getInputStream0(Unknown Source)
at sun.net.www.protocol.http.HttpURLConnection.getInputStream(Unknown Source)
at hudson.model.UpdateCenter$UpdateCenterConfiguration.download(UpdateCenter.java:757)
... 6 more
Caused by: java.io.FileNotFoundException: http://mirrors.jenkins-ci.org/war/1.625/jenkins.war
at sun.net.www.protocol.http.HttpURLConnection.getInputStream0(Unknown Source)
at sun.net.www.protocol.http.HttpURLConnection.getInputStream(Unknown Source)
at sun.net.www.protocol.http.HttpURLConnection.getHeaderField(Unknown Source)
at java.net.URLConnection.getHeaderFieldLong(Unknown Source)
at java.net.URLConnection.getContentLengthLong(Unknown Source)
at java.net.URLConnection.getContentLength(Unknown Source)
at hudson.model.UpdateCenter$UpdateCenterConfiguration.download(UpdateCenter.java:756)
... 6 more