You should rather clean or smooth the source point data than generate a TIN or raster and try to clean later.
Using ArcGIS
Note that LAS data handling has greatly improved in ArcGIS 10.2. If 10.2 (with 3D Analyst) is available to you, try the build-in functions:
There is a tool called Locate Outliers (part of 3D Analyst) which works perfectly for removing spikes and such. Judging from the screenshot you provided this will most probably clean your spikes.
As your spikes seem to align, you could also use the Profile tool and carefully cut outliers manually along a swath profile.
For a more sophisticated filtering, you can classify your Lidar Point Cloud data (3D Analyst -> Set LAS Class Codes Using Features) and build your TIN using a subset of points (e.g. only points classified as surface).
Using other tools than ArcGIS
You could use FUSION Lidar Toolkit (open source), SAGA GIS (open source), LasTools (some parts require commercial licensing; ArcGIS Toolbox provided) or GlobalMapper/Lidar (also commercial) to manipulate your Point Cloud data.
If you prefer filtering a raster dataset, you can apply a median filter to eliminate spikes, but I highly recommend to filter your source pont cloud instead. Especially if your points are unevenly distributed, a single outlying point in a less dense area can produce a more widespread error in a corresponding raster dataset.
Best Answer
You can't add basemaps into ArcScene
from Adding an ArcGIS Online basemap into ArcGlobe
You could work around this by clipping or exporting a basemap as an image and adding the image to your ArcScene.
I would, however, recommend you look into using ArcGIS Pro rather than ArcScene. ArcGIS Pro will allow you to make use of basemaps, and can be used as a local scene (similar to ArcScene) or as a global scene (similar to ArcGlobe), as well as a 2D map view. In fact you can do all three at the same time within the same ArcGIS Pro document.
The screenshot below shows a local scene in ArcGIS Pro, and the option to add/change basemaps.