May be I already observed similar effects. When I want to paste something, mostly from not AOO source documents, after 'copy' the 'paste' icon does not offer the expected options, even may be greyed out. Often, but not reliabley, at least menu 'Edit -> Paste special' offers the required paste options. But until now I am far away from knowing how to make the problem reproducible.

@Ken:
Thank you for your feedback – unfortunately important information we will 
need to reproduce your problem is missing.
Please add all information requested in following:
a) Write a meaningful Summary describing exactly what the problem is
   Not: "everything impossible" but "menu 'Edit -> Paste Special' 
  inaciteve (greyed out)
b) Attach a test kit with source document  or refer to an existing 
   sample document in an other Bug with a link; to attach a file to this 
   bug report, just click on "Add an attachment" right on this page.
   If you want to attach a test kit with multiple documents zip them into
   a single testkit.zip and attach the  testkit.zip
c) Contribute a document related step by step instruction containing every 
   key press and every mouse click how to reproduce your problem 
d) Attach screenshots with comments if you believe that that might explain the 
   problem better than a text comment. Best way is to insert your screenshots
   into a DRAW document and to add comments that explain what you want to show
e) if possible contribute an instruction how to create a sample document 
   from the scratch
f) add information 
   f1) what EXACTLY is unexpected (see above) 
   f4) concerning your Operating System (Version, Distribution, Language)
   f5) concerning your AOO version (with Build/revision ID if it's not a 
      public release) and localization (UI language, Locale setting)
   f6) AOO settings that might be related to your problems 
      (video hardware acceleration, ...)
   f7) how you launch AOO and how you opened the sample document
   f8) Whether your problem persists after you have renamed your user profile 
     (Quit Quickstart before!) before you launch AOO (please see   <https://wiki.openoffice.org/wiki/Documentation/How_Tos/Handling_the_OpenOffice.org_User_Profile>
     <https://wiki.documentfoundation.org/User_Profile#Mac_OS_X>
   f9) Whether that worked in former OOO / AOO Versions 

Please do not cite these hints in your reply, but cite the items like:
f7): Desktop-icon for soffice.exe / AOO File menu -> Open	Thank you for your feedback – unfortunately important information we will 
need to reproduce your problem is missing.

I can reproduce this Bug.
This bug can also be expanded further. 1) Paste function with options is not working not for below kinds of documents.
1) Paste function with options is not working from Online documents. (PDF, Google Drive, Online word documents.)
2) Paste function with options is not working from same .ODT documents. 
3) It is not happening when we use Cut+Paste option ; but similar effects appears when it comes to Copy+paste option.
3) Ultimately , paste option is not showing whether they are 1) Cut 2) Copy.
4) When we see overview with the Paste Function in all the below versions (<4.1.1) paste function is not allowing to set the options.
Please find below link for the Open Office Standards. 
https://www.openoffice.org/dev_docs/features/
This link is below for open office for 3.2 Version. [Specific]
https://www.openoffice.org/dev_docs/features/3.2/rc1.html#calc_paste

May 2, 2015 - I was unable to duplicate this issue.

Environment/Software versions:  
Windows 8.1 (on an Asus SonicMaster laptop)
OpenOffice 4.0.1 (AOO401m5(Build:9714)
Rev. 1524958 2013-09-20 11:40:29 
(Fr, 20 Sep 2013) 

Steps used to test:

1-Create and save a new OpenOffice Writer document
2-Save the document
3-Open http://www.publicbookshelf.com/mystery/sherlock-holmes/scandal-bohemia (to use for copy
4-Copy a section of text from website using cntrl-c
5-Paste into OO document using cntrl-v 
6-Return to website, highlight a section of text, right-click, select copy
7-Return to the OO document, use right-click, paste
8-Remaining in the OO document, select the paste icon from the tool bar and paste the buffer into the document again

1-Open a .pdf file and repeat steps 1-8
2-Return to the .pdf, highlight a large section of data (including pics/graphics/links) then select cntrl-x
3-Paste using cntrl-v into OO document

1-Open a GoogleDocs file and repeat steps 1-8
2-Return to the GoogleDocs file, highlight a large section of data (including pics/graphics/links), then select cntrl-c
3-Paste using paste icon from the tool bar into OO document

Select a large section of text to cut and paste from one of the above documents into the OO document

During the above steps I was expecting to see the copy/paste functionality (whether from the tool bar, mouse-clicks or contrl keys) to become disabled - this did not occur.

Environment:  
Windows 7 Professional (HP, Intel core i3 laptop)
Processor: Intel (R) Core (TM) i3-4010U CPU @ 1.70GHz  1.70GHz
Ram: 4.00 GB, 64-Bit Operating System 
Open Office 4.2.0

I have tried to reproduce the issue and also noticed some information is missing in the report for example:
•	A screen shot would have helped if added with comments as to what Ken wants. 
•	What version did Ken worked on.
•	What OO setting s were in place


Steps I used to reproduce:
•	Create a word document and open it in OO
•	Open any web page using chrome/IE/Firefox etc
•	Select some excerpt and press ctrl+c at once
•	Paste it on the Open office document that we just saved with ctrl+v

Furthermore: 

•	copy some excerpt from same website using right click option (without using ctrl+c option)and paste this on document using right click paste option 
•	Paste onto the OO document, use right-click, paste

(Andreas Nielsen, May 4 2019)

I was unable to reproduce this issue using version 4.5.0.
I was also unable to reproduce this issue using version 4.0.1.

Both installations were done with typical/default settings.

Apache OpenOffice 4.5.0 (AOO450m1(Build:9900) - Rev. 1858450)

Apache OpenOffice 4.0.1 (AOO401m5(Build:9714)  -  Rev. 1524958) 2013-09-20 11:40:29 (Fr, 20 Sep 2013)

HP ZBook 17 G2
Windows 10 Pro, Version 1803
Processor: Intel (R) Core (TM) i7-4810MQ CPU @ 2.80GHz
Ram: 24.00 GB, 64-Bit Operating System

I was able to successfully complete all of these steps in both versions:
* Paste text copied from PDF document viewed in Google Drive.
* Paste text copied from PDF document viewed directly within Chrome (local file).
* Paste text copied from PDF document viewed directly within Chrome (online file).
* Paste text copied from an online Word document.
* Paste text copied from online book viewer (http://www.publicbookshelf.com/mystery/sherlock-holmes/scandal-bohemia - Shared by Elmer).

Closing issue due to comment #5