Permission issues when deploying Sitecore 8 site causing some functionality to fail?

I've recently deployed a site at a client location and they are experience strange behavior with some functionality not working that can't be reproduced locally even when running a backup of their databases locally.

Symptoms:

It isn't possible to Unlock All items from the dialog, it simply spins forever with no errors in the log or in the network inspector

When attempting to unlock a single item sometimes an error appears after a long wait:

[DETAILS]

job in checkstatus
Description: An unhandled exception occurred during the execution of the current web request. Please review the stack trace for more information about the error and where it originated in the code.

Exception Details: System.InvalidOperationException: job in checkstatus

Source Error:
An unhandled exception was generated during the execution of the current web request. Information regarding the origin and location of the exception can be identified using the exception stack trace below.

Stack Trace:

[InvalidOperationException: job in checkstatus]

Sitecore.Shell.Applications.Dialogs.Progress.ProgressPage.CheckStatus() +329

[TargetInvocationException: Exception has been thrown by the target of an invocation.]

System.RuntimeMethodHandle.InvokeMethod(Object target, Object[] arguments, Signature sig, Boolean constructor) +0

System.Reflection.RuntimeMethodInfo.UnsafeInvokeInternal(Object obj, Object[] parameters, Object[] arguments) +229

System.Reflection.RuntimeMethodInfo.Invoke(Object obj, BindingFlags invokeAttr, Binder binder, Object[] parameters, CultureInfo culture) +193

Sitecore.Web.UI.XamlSharp.Xaml.XamlControl.ExecuteAjaxMethod(AjaxMethodEventArgs e) +184

Sitecore.Web.UI.WebControls.AjaxScriptManager.DispatchMethod(Control control, String parameters) +423

Sitecore.Nexus.Pipelines.NexusPipelineApi.Resume(PipelineArgs args, Pipeline pipeline) +398

Sitecore.Pipelines.Pipeline.Start(PipelineArgs args, Boolean atomic) +327

Sitecore.Web.UI.WebControls.ContinuationManager.RunPipelines() +255

Sitecore.Web.UI.WebControls.ContinuationManager.OnPreRender(EventArgs e) +226

System.Web.UI.Control.PreRenderRecursiveInternal() +113

System.Web.UI.Control.PreRenderRecursiveInternal() +222

System.Web.UI.Control.PreRenderRecursiveInternal() +222

System.Web.UI.Page.ProcessRequestMain(Boolean includeStagesBeforeAsyncPoint, Boolean includeStagesAfterAsyncPoint) +4297

[/DETAILS]

Uploading images into the media library fail with a strange exception:

Also, when attempting to use WFFM, none of the web bar buttons will open a dialog and fail silently.

There are also issues with the Package installation wizard showing blank screens (again with no errors in network inspector and nothing in the sitecore log).

The site was deployed on Windows Server 2012 R2, IIS 8.5. I obtained a list of permissions on the site folder which you can see below:

There are also no extra modules running on the server like UrlScan or anything like that, just the defaults.

If you have any thoughts or suggestions on how you would tackle this, it would be appreciated