Assigning to a property might have side effects that make it necessary to make two successive assignment, e.g.:

procedure RestartTimer;
begin
FTimer.Enabled := False;
FTimer.Enabled := True;
end;

Difficult to determine whether this is a problem or not.
Maybe we could have a special comment like this:

// FixInsight:NoW512: duplicate assignment necessary
// ^- this part for FixInsight ^- This part for the developer

to get rid of these warnings once we have checked them?

So, this would no longer raise this warning:

procedure RestartTimer;
begin
// FixInsight:NoW512: duplicate assignment necessary
FTimer.Enabled := False;
FTimer.Enabled := True;
end;

Function MyFunc:String;
Begin
  MyFunc:='dummy';
End;

I have a few functions where the result type is a record.
In some of these functions, the following construct is used:

with Result do
begin
  Field1 := '';
  Field2 := 0;
end;

In this case, Result is indeed assigned to.

Enabling for example only the W513 warning requires me to disable a lot other warnings and I guess the amount grows over time. A popupmenu with something like "Disable All" and "Enabled All" would be very helpful.

It would be nice to be able to ignore a block of code rather than only a single line for a particular or even all warnings. Something like this:

//FI:all off - turn off all warnings
some code here
//FI:all on - turn on warnings again

or
// FI:W508 off - ignore empty procedures
lots of empty procedures here
// FI:W508 on - warn about empty procedures again

Probably most frequent error:
(a = 1 OR b = 2) AND c = 3 OR d = 4
In general:
(*lower precedence op*) *higher precedence* *lower precedence op*
or without parentheses:
*lower precedence op* *higher precedence* *lower precedence op*

Methods that add for example items to a list may lead to a false positive W508 warning

Sample code:

type
  TItem = class(TObject)
    Prop: Boolean;
  end;

  TItemList = class(TObject)
  public
    function Add: TItem;
  end;

function TItemList.Add: TItem;
begin
{
  FItems.Add(TItem.Create);
  Result := FItems.Last;
}
end;

procedure Test;
var
  List: TItemList;
begin
  List.Add.Prop := False;
  List.Add.Prop := False;//<- W508 Variable is assigned twice successively
end;

Also when Add has a parameter (e.g. AName) and both Add calls have the same value then W508 occurs.

If you resize the 'Run FixInsight' dialog (the one that shows all the possible messages, lets you check / uncheck them, etc) then the button stay in the same position. They should be anchored to the bottom right or similar.