With the recent fixes to bug #63931, this too looks fixed. Closing as fixed. If you have problems, comment here and it can be reopened. It'll be in Octave 8.2.0 to be released next week if all goes well.

I ran your code and this is the output I got with both the unpatched and patched versions, so this looks like good news?

octave:1> test_63968
Writing File
Wrote 16386810 bytes

File Pointer 16386810

Write took 95.057924 seconds

Reading File
Read took 0.087963 seconds

Read 16386810 bytes

File Pointer 16386810

Reading File
Read took 141.914758 seconds

Read 16386810 bytes

Then to double-check, I set the encoding to latin1, and sure enough I got the error:

octave:1> __mfile_encoding__ ("latin1")
octave:2> __mfile_encoding__
ans = latin1
octave:3> test_63968
Writing File
Wrote 16386810 bytes

File Pointer 16277485

Write took 99.510554 seconds

Reading File
Read took 0.088034 seconds

Read 16277511 bytes

File Pointer 16277511

Reading File
Index 254 Index 76 Index 251 Read Failure

File Pointer 16277511

error: Invalid Read
error: called from
    test_63968 at line 49 column 9

This is identical to the other two bugs, so I'll leave this closed as a duplicate but if you want a workaround before 8.2.0 is released, please set your encoding to UTF-8. You can do that in the Octave GUI, or from the command prompt you can run

__mfile_encoding__ ("utf-8")

Seems to be a few bugs with fwrite.  Not only is it writing incorrect data when you do binary writes with uint8, but it also seems to be writing an incorrect number of bytes and not reporting a write error.

Run the following script.  It does not report a write error, but when you read the data back it has a different amount of bytes.

display("Writing File");
ID = tic();
fid = fopen("TestWrite","w");
for i = 1:255
  for j = 1:254
    for k = 1:253
      CNT = fwrite(fid,uint8(k),"uint8");
      if (CNT == 0)
        display(sprintf("Index %d Index %d Index %d Write Failure\n",i,j,k));
        error("Write Error");
      endif
    endfor
  endfor
endfor
WRITE_FP = ftell(fid);
display(sprintf("Wrote %d bytes\n",i*j*k));
display(sprintf("File Pointer %d\n",WRITE_FP));
fclose(fid);
elapsed_time = toc(ID);
display(sprintf("Write took %f seconds\n",elapsed_time));
##
## Read back Data
##
display("Reading File");
ID = tic();
fid = fopen("TestWrite","r");
DATA = uint8(fread(fid,"uint8"));
READ_FP = ftell(fid);
fclose(fid);
elapsed_time = toc(ID);
display(sprintf("Read took %f seconds\n",elapsed_time));
display(sprintf("Read %d bytes\n",length(DATA)));
display(sprintf("File Pointer %d\n",READ_FP));
##
## Read Back Data - Method 2
display("Reading File");
ID = tic();
fid = fopen("TestWrite","r");
DATA2=uint8([]);
for i = 1:255
  for j = 1:254
    for k = 1:253
      [VAL, CNT] = fread(fid,1,"uint8");
      if (CNT == 0)
        READ2_FP = ftell(fid);
        display(sprintf("Index %d Index %d Index %d Read Failure\n",i,j,k));
        display(sprintf("File Pointer %d\n",READ2_FP));
        error("Invalid Read");
      endif
      DATA2(i*j+k) = uint8(VAL);
    endfor
  endfor
endfor
fclose(fid);
elapsed_time = toc(ID);
display(sprintf("Read took %f seconds\n",elapsed_time));
display(sprintf("Read %d bytes\n",length(DATA)));