I second Motorhead's suggestion of checking grounding connections, and the connections on the alternator, too. Did you clean the connections and use dielectric grease when you replaced it? Dielectric grease is often overlooked when doing electrical work, but it really does help to make a good connection and makes plugs easier to pull apart. I use a Q-tip. Dip one end in rubbing alcohol to clean the connection, then use the other end to apply the grease.

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1982 300D, black w/ palomino leather, 203K
2001 E320, champagne, 105K (Mom's)
1999 Dodge Dakota, squeaky & battered, 142K