I just bought a new 4003 (2016) and been having issues with the E saddle since it arrived. I mentioned when I took it to have set up done (strings changed to DUNLOP 50 - 105 and tuned to E flat) that saddle is not sitting flush and wobbles. Still does it (not sure if they even looked at it, the tech was away when I picked it up) and the E string sounds really flat on the seventh fret. Not sure if he did a truss rod adjustment.

Even when it's tuned, I can lift the E string off the saddle and the saddle wobbles side to side. Does this sound like I have a defective saddle? Maybe the saddle isn't cut deep enough? Did the same with the stock Ric strings. The A string even makes the E string saddle rattle a bit when playing.

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2008 4004ii Mapleglo
2016 4003 Mapleglo
Marshall Stack

Search the threads. Wobbly saddles have happened. I don't remember what the fix was, but it's in the threads somewhere.

You can lift the string out of the grooves on any old style guitar or bass. They are just not cut that deep.
Early Fenderbasses didn´t have any grooves at all. Then they used saddles that were like cut-up screws. If you take the string of a Fender saddle then it will be rockin and wobblin back and forth and even twist and flip upside down. It´s the tuned string that holds it in place.
But if it´s rockin back and forth then maybe the grooves in the screw that adjusts the intonation, or in the saddle, are bad and need to be replaced. But if you bought it new and can proove I´m sure RIC will send some new ones. I think that was the fix in one of the earlier cases.

The older bridges had saddle wobble because the hole in the saddle for the adjustment screw was too high. This would make the saddle sit a bit high & rock side to side. Rickenbacker updated the saddles & the problem went away. The fix was to drill the hole in the bridge slightly larger, allowing the saddle to sit lower. You would need to determine if the saddle was the problem or if the hole in the bridge is too high. If the bass is under warranty I would call customer service & see what they can do for you. If not under warranty, take a saddle that doesn't wobble & try it in the E-hole (couldn't resist). If it's flush it's the saddle. If not, it's the hole in the bridge. Good luck.

Good Morning & Happy Thanksgiving !!
My suggestion to you firstly would be to return the Bass back to where you purchased it and exchange it for another NEW BASS. If that doesn't work out for you can try a Replacement Bridge. Here's a good choice:
http://www.bestbassgear.com/hipshot-4-s ... bridge.htm
This is a DIRECT replacement for the Stock bridge. I've replaced the bridges on 4 Rick 4003's with excellent results. Easy to install...No Extra Drilling & a Direct Replacement.