Experienced the same error ("Invalid LatLng object: (NaN, NaN)") with a freshly installed module just now. In my case it was caused by a legacy (?) Nominatim URL:
The module uses https://nominatim.openstreetmap.org/search/?q=Berlin&limit=5&format=json&addressdetails=1&json_callback=_l_geocoder_2, but Nominatim responded with a 404 error. I had to remove the trailing slash from 'search/' in modules/FieldtypeLeafletMapMarker/Control.Geocoder.js, line 343. Change this line from:
L.Control.Geocoder.jsonp(this.options.serviceUrl + 'search/', L.extend({
To:
L.Control.Geocoder.jsonp(this.options.serviceUrl + 'search', L.extend({
Now the modules uses the correct Nominatim URL, in this example: https://nominatim.openstreetmap.org/search?q=Berlin&limit=5&format=json&addressdetails=1&json_callback=_l_geocoder_2
The map loads fine, with the initial marker.