How to judge the reputability of a journal that seems to be of poor quality, but has a distinguished editorial board? I happened to visit the website of the IJDEA (International Journal of Differential Equations and Applications) and was wondering – how good is this journal? There was a question here on Academia. SE regarding IJPAM (International Journal of Pure and Applied Mathematics, by the same publisher: Academic Publications Ltd.) and it seems this journal is not up to the mark. 

However, IJDEA's Editorial Board has some prominent members from reputed institutions that I just couldn't overlook. For instance:


E.W. Cheney and R.E. Showalter from UT Austin, USA
S.N Chow from the National University of Singapore, Singapore
E DiBenedeto from Northwestern University, USA
A. Fokas from the University of Cambridge, UK
J. Marsden from CalTech, USA
(Late) P.A. Samuelson from MIT, USA 
C.W. Shu from Brown University, USA


My question is: Given the presence of such top-class scientists on its editorial board, why are IJPAM/IJDEA and Academic Publications Ltd. considered predatory by Beall's list?

P.S.: I'm assuming that the Editorial Board and quality of articles should be good enough to check the quality of the journal. Please correct me in case I'm wrong.
You've already identified part of the problem:


Deceased individuals like Paul Samuelson and Ilya Prigogine should not be listed as "editors" of a normal journal.
The editor-in-chief of the journal should be clearly identified.
They're claiming to have an Impact Factor when they're not indexed by the services that publish Impact Factors


You can see Beall's full list of criteria on his blog Scholarly Open Access.