Static Content Loading issue when Upgrade From Magento 2.1.0 to Magento 2.1.3

Reason:-

There was no RewriteBase in directory pub/static/ and Apache could not find the files because searched for them from the root folder. After it added: RewriteBase /pub/static everything start working. 

Solution 1:-
The rewrite should work:

RewriteRule ^version.+?/(.+)$ $1 [L]

add above line in .htaccess file (pub/static).your .htaccess file should look like this.

If you are running apache change in .htaccess file (pub/static)

<IfModule mod_rewrite.c>

    RewriteEngine On

    RewriteBase /pub/static

    # Remove signature of the static files that is used to overcome the browser cache

    RewriteRule ^version.+?/(.+)$ $1 [L]

    RewriteCond %{REQUEST_FILENAME} !-f

    RewriteCond %{REQUEST_FILENAME} !-l

    RewriteRule .* ../static.php?resource=$0 [L]

</IfModule>

 Solution 2:-

Magento 2.1.3 release assumes the default value for Stores => Configuration => Developer => Static Files Settings => Sign Static Files is set to Yes.

So instead of changing the rewrites, its possible to set this feature to No.

Solution 3:-
Change sign static files to Yes from admin, because the admin fails to load the frontend assets, change/add this setting in the core_config_data table:

scope: default
scope_id: 0
path: dev/static/sign
value: 0
or run this query

INSERT INTO `core_config_data`(`path`, `value`) VALUES ('dev/static/sign', 0) ON DUPLICATE KEY UPDATE `value`=0

you can check this issue here https://github.com/magento/magento2/issues/7869,
Solution :-  
If you are running Nginx then update server config file with this

location /static/ {

    # Uncomment the following line in production mode

    # expires max;

    # Remove signature of the static files that is used to overcome the browser cache

    location ~ ^/static/version {

        rewrite ^/static/(version\d*/)?(.*)$ /static/$2 last;

    }

    location ~* \.(ico|jpg|jpeg|png|gif|svg|js|css|swf|eot|ttf|otf|woff|woff2)$ {

        add_header Cache-Control "public";

        add_header X-Frame-Options "SAMEORIGIN";

        expires +1y;

        if (!-f $request_filename) {

            rewrite ^/static/(version\d*/)?(.*)$ /static.php?resource=$2 last;

        }

    }

    location ~* \.(zip|gz|gzip|bz2|csv|xml)$ {

        add_header Cache-Control "no-store";

        add_header X-Frame-Options "SAMEORIGIN";

        expires    off;

        if (!-f $request_filename) {

           rewrite ^/static/(version\d*/)?(.*)$ /static.php?resource=$2 last;

        }

    }

    if (!-f $request_filename) {

        rewrite ^/static/(version\d*/)?(.*)$ /static.php?resource=$2 last;

    }

    add_header X-Frame-Options "SAMEORIGIN";

}