Currently term store operations are only available via JSOM. It would be nice to see this added to the REST API as well.

Support .NET Core with CSOM

Please provide subscriptions API (_api/Web/Lists('listID')/subscriptions support (WebHooks)) SharePoint 2016 On-Premise which helps in webhooks, desktop notifications, mobile/push notifications and cross platform notifications to name a few.

App-only policy in the SharePoint App Model is very restricted regarding Taxonomy operations. Even if an app is granted full control over the tenant, it lacks the permission to do anything but read operations on Taxonomy. Please provide the ability to create Groups, Term Sets and terms using app-only policy.

Provide option to enable\disable event firing from Remote Event Receivers in SharePoint Online (CSOM/API) similar to SSOM - EventFiringEnabled

Actually, the only way to paginate list items using the new REST APIs is to use __next property. There's no way to have a full working pagination using $top and $skip token as for any other REST call.
See my comment here:
http://msdn.microsoft.com/library/d4b5c277-ed50-420c-8a9b-860342284b72.aspx

It is actually possible to import the definition of a XsltListViewWebPart via LimitedWebPartManager in CSOM. However, not all properties are supported. Important properties like XmlDefinition, Toolbar, ViewStyle, .. are being ignored. There's no possibility to have everything set correctly not even manipulating the backed view after importing the WebPart. Please read also this discussion:
http://sharepoint.stackexchange.com/questions/90433/add-document-library-xsltlistviewwebpart-using-csom-or-web-services

There's an undocumented API (https://tenant.sharepoint.com/_vti_bin/homeapi.ashx/ ) to follow sites and query data around those concepts. For corporate intranet scenarios, we often want to present the data a different way, surfacing native SharePoint capabilities. In order to add a "follow" button on an SPFX web part, we'd need an API to access that.

Related GitHub issue https://github.com/SharePoint/sp-dev-docs/issues/1689

REST API should be fixed when getting single value Managed Metadata since it returns the Id instead of the actual value, which then requires another call to get the value. Without this you cannot show a list of items/docs with the single Managed Metadata value. Note that "Allow Multiple" Managed Metadata works fine as it returns a collection of actual values.

For details see: http://sharepointificate.blogspot.com/2014/05/taxonomy-columns-sharepoint-2013-list.html

When creating Site Collections through CSOM and providing an LCID. (For example 2067) an exception is thrown.

[Quote]
SiteCreationProperties.Template\r\nParameter name: Specified value is not supported for the SiteCreationProperties.Template parameter." is thrown at ExecuteQuery();
[/Quote]

The Exception is also not pointing in the right direction.
1) It should be possible to create Site Collections providing the LCID
2) When an Invalid Lcid is passed, the exception should point in the right direction.

List items that have an Audience field attached should be audience filtered when retrieved via the REST API.

For example, a list that has link items with the Audience field attached to target particular items at particular groups of people. If the REST APIs are used to retrieve items from this list, then the identity of the requesting user should be optionally used to filter the results based on audience.

Please consider adding support for setting/retrieving doucment set properties on a content type. We need to be able to set properties like Shared columns, Welcome page and Welcome page view on the document set.

The Web class in the CSOM lacks the ability to send a web to the recycle bin. Currently it's only possible to delete a web by using Web.DeleteObject() which makes restoring from recycle bin impossible.

Please consider adding a Recycle() method to the Web class.

Right now there is no API to check that. If you add a security group into a SharePoint group, there is no way to check if the current user is a part of the SharePoint group: The user is not listed in the group.Users and the SharePoint group is not listed in the user.Groups. The 3 APIs that allowed to do this in full trust code are missing from CSOM so we need an alternative.

Remote event receivers can currently, in SharePoint Online, not be added to content types (https://msdn.microsoft.com/en-us/library/microsoft.sharepoint.client.contenttype_members.aspx). This makes it somehow tedious to catch events that are fired from items of a specific content type is added/updated/deleted. Having the possibility to add an event receiver to a content type would make this scenario easier to implement.

Some list/library settings are available via CSOM. Others are available via the list property bag (although that approach is not desirable). However, there are even other advanced settings that don't appear to be accessible (read or write) via CSOM/REST. In particular, the advanced settings for "open documents in the browser" (open in the client application, etc.) or allow "quick edit" (yes/now).

I'm looking at SharePoint 2013 when trying to do this, but I suspect the same problem occurs for SharePoint Online and SharePoint 2016.

Allow REST clients to update list items a la SystemUpdate. That is, REST clients should be able to update list item metadata without creating a new version and without affecting system columns like authors and timestamps. The same idea for CSOM was recently implemented and I'm puzzled why the REST API is always left behind.
The CSOM idea:
https://sharepoint.uservoice.com/forums/329220-sharepoint-dev-platform/suggestions/15147093-enable-listitem-systemupdate-via-csom